For Class 8, 9 & 10
Master the basics - and everything after gets easier
Concept-first questions with clear model answers in Physics, Chemistry, Maths and Biology, all NCERT-aligned. Start early, build the habit, and walk into your boards, NEET and JEE already ahead.
Interactive lessons
learn by playingDrag, slide and build - watch each concept come alive, then reveal the answer.
200 interactive lessons
Ohm's law
Class 10 Physics
Slide V & R, watch the bulb glow
Open →pH scale
Class 10 Chemistry
Slide across acids and bases
Open →Atomic number and mass number
Class 9 Chemistry
Add protons & neutrons, build shells
Open →Laws of reflection
Class 8 Physics
Change the angle, watch it bounce
Open →Volume of a sphere
Class 9 Maths
Grow the radius, see the volume
Open →Area of a trapezium
Class 8 Maths
Drag the sides, read the area
Open →Power of a lens
Class 10 Physics
Move the object, trace the rays
Open →Food chain and energy flow
Class 10 Biology
Follow the energy as it flows
Open →Speed
Class 8 Physics
Slide distance & time, watch the speed
Open →Density
Class 9 Physics
Pack mass into volume, float or sink
Open →Work done
Class 9 Physics
Push harder or farther, watch work grow
Open →Kinetic energy
Class 9 Physics
Speed it up - energy grows with the square
Open →Power of a lens
Class 10 Physics
Shorten the focal length, boost the power
Open →Mole concept
Class 9 Chemistry
Weigh out grams, count the moles
Open →Avogadro's number
Class 9 Chemistry
Add moles, count the particles
Open →Microscope magnification
Class 8 Biology
Grow the image, read the magnification
Open →Population density
Class 10 Biology
Add individuals, shrink the land, see crowding
Open →Simple interest
Class 8 Maths
Slide money, rate & time, watch interest
Open →Pythagoras theorem
Class 9 Maths
Stretch the two sides, get the hypotenuse
Open →Probability of an event
Class 10 Maths
Change the outcomes, watch the odds
Open →Newton's second law
Class 9 Physics
Push a mass, pick an acceleration
Open →Momentum
Class 9 Physics
Slide mass & velocity, build momentum
Open →Pressure
Class 8 Physics
Shrink the area, feel the pressure rise
Open →Weight
Class 9 Physics
Change the planet's gravity, watch your weight
Open →Refractive index
Class 10 Physics
Slow light in the medium, raise the index
Open →Resistors in series
Class 10 Physics
Add two resistors in a line
Open →Mass percentage of a solution
Class 9 Chemistry
Dissolve solute, read the strength
Open →Concentration of a solution
Class 9 Chemistry
Pack solute into less liquid
Open →Population change
Class 10 Biology
Balance births against deaths
Open →Compound microscope
Class 8 Biology
Combine eyepiece & objective lenses
Open →Area of a circle
Class 8 Maths
Grow the radius, watch the area square
Open →Volume of a cuboid
Class 8 Maths
Stretch length, breadth & height
Open →Electronic configuration and valency
Class 9 Chemistry
Slide the atomic number, build the atom
Open →Homologous series (alkanes)
Class 10 Chemistry
Add carbons, name the compound
Open →Mass number
Class 9 Chemistry
Add protons & neutrons, get the mass number
Open →Power
Class 9 Physics
More work in less time = more power
Open →Potential energy
Class 9 Physics
Lift a mass higher, store energy
Open →Wave speed
Class 9 Physics
Tune frequency & wavelength, set the speed
Open →Electric current
Class 10 Physics
Push charge per second, get the current
Open →Percentage
Class 8 Maths
Compare part to whole as a %
Open →Electron dot structure
Class 9 Chemistry
Draw valence electrons as dots
Open →Acceleration
Class 9 Physics
Speed up over time, find acceleration
Open →Distance, speed and time
Class 8 Physics
Set speed & time, cover the distance
Open →Frequency and time period
Class 9 Physics
Shorten the period, raise the frequency
Open →Heating effect of current
Class 10 Physics
Raise the current, watch heating soar
Open →Area of a triangle
Class 8 Maths
Set base & height, halve the rectangle
Open →Area of a rectangle
Class 8 Maths
Set length & breadth, fill the area
Open →Mean (average)
Class 9 Maths
Share the total equally across items
Open →Discount
Class 8 Maths
Slide price & % off, see the saving
Open →Heart rate
Class 10 Biology
Set heart rate & time, count the beats
Open →Resistors in parallel
Class 10 Physics
Wire two resistors side by side
Open →Electric charge
Class 10 Physics
Flow current over time, collect charge
Open →Electrical energy and units
Class 10 Physics
Run appliances, add up the units
Open →Kelvin temperature scale
Class 9 Chemistry
Slide Celsius, read the Kelvin
Open →Moles from number of particles
Class 9 Chemistry
Divide particles by Avogadro's number
Open →Ten percent law
Class 10 Biology
See 10% of energy reach the next level
Open →Area of a square
Class 8 Maths
Grow the side, square the area
Open →Volume of a cube
Class 8 Maths
Grow the edge, cube the volume
Open →Circumference of a circle
Class 8 Maths
Grow the radius, roll out the rim
Open →Surface area of a cube
Class 9 Maths
Grow the edge, cover six faces
Open →Potential difference
Class 10 Physics
Share work across charge, get volts
Open →Resistance from Ohm's law
Class 10 Physics
Divide voltage by current, get resistance
Open →Echo and SONAR
Class 9 Physics
Time the echo, find the distance
Open →Mass from moles
Class 9 Chemistry
Multiply moles by molar mass
Open →Breathing rate
Class 10 Biology
Set breathing rate & time
Open →Volume of a cylinder
Class 10 Maths
Set radius & height, fill the can
Open →Compound interest
Class 8 Maths
Compound money over years
Open →Profit and loss percentage
Class 8 Maths
Set cost & selling price, see profit %
Open →Perimeter of a rectangle
Class 8 Maths
Set length & breadth, walk the border
Open →Surface area of a sphere
Class 10 Maths
Grow the radius, wrap the ball
Open →Time period
Class 9 Physics
Raise the frequency, shrink the period
Open →Relative velocity
Class 9 Physics
Two objects approach - add their speeds
Open →Average velocity
Class 9 Physics
Average the start and end speeds
Open →Equations of motion (v = u + at)
Class 9 Physics
Accelerate from u for a time t
Open →Kelvin to Celsius
Class 9 Chemistry
Slide Kelvin, read the Celsius
Open →Population growth rate
Class 10 Biology
Balance births vs deaths per population
Open →Perimeter of a square
Class 8 Maths
Grow the side, walk four edges
Open →Perimeter of a triangle
Class 8 Maths
Add the three sides
Open →Area of a parallelogram
Class 8 Maths
Set base & height, slide the shape
Open →Area of a rhombus
Class 8 Maths
Set the two diagonals
Open →Equations of motion (distance)
Class 9 Physics
Start, accelerate, cover ground
Open →Joule's law of heating
Class 10 Physics
Raise current, resistance or time
Open →Electric power (P = VI)
Class 10 Physics
Multiply voltage by current
Open →Average atomic mass of isotopes
Class 9 Chemistry
Mix two isotopes by abundance
Open →Seed germination percentage
Class 9 Biology
Count sprouted seeds out of the total
Open →Volume of a cone
Class 9 Maths
Set radius & height, fill the cone
Open →Surface area of a cylinder
Class 9 Maths
Wrap the side and both ends
Open →Surface area of a cuboid
Class 9 Maths
Cover all six rectangular faces
Open →nth term of an AP
Class 10 Maths
Step from the first term by d
Open →Sum of an AP
Class 10 Maths
Add up the first n terms
Open →Focal length of a mirror
Class 10 Physics
Halve the radius to find the focus
Open →Speed of light in a medium
Class 10 Physics
Raise the index, slow the light
Open →Percentage purity
Class 9 Chemistry
Weigh the pure part of a sample
Open →Slope of a line
Class 10 Maths
Rise over run gives the steepness
Open →Percentage change
Class 8 Maths
Compare a new value to the old
Open →Volume of a hemisphere
Class 9 Maths
Grow the radius of half a ball
Open →Area of a sector
Class 10 Maths
Cut a slice of angle from a circle
Open →Length of an arc
Class 10 Maths
Measure the curved edge of a slice
Open →Slant height of a cone
Class 9 Maths
Combine radius & height for the slant
Open →Unit conversion (km/h to m/s)
Class 9 Physics
Convert km/h into m/s
Open →Equations of motion (v^2 = u^2 + 2as)
Class 9 Physics
Accelerate over a distance, find v
Open →Impulse
Class 9 Physics
Hit harder or longer, change momentum
Open →Wavelength
Class 9 Physics
Speed over frequency gives wavelength
Open →Oscillations
Class 9 Physics
Vibrate at a frequency for a time
Open →Cost of electricity
Class 10 Physics
Units times rate gives the bill
Open →Number of neutrons
Class 9 Chemistry
Take protons away from the mass number
Open →Curved surface area of a cone
Class 9 Maths
Wrap the slanted side of a cone
Open →Total surface area of a cone
Class 9 Maths
Add the base circle to the cone's side
Open →Curved surface area of a hemisphere
Class 9 Maths
Cover the dome of a hemisphere
Open →Diagonal of a square
Class 9 Maths
Cross a square corner to corner
Open →Unit conversion (m/s to km/h)
Class 9 Physics
Convert m/s into km/h
Open →Distance from velocities
Class 9 Physics
From two speeds, find the distance
Open →Diagonal of a rectangle
Class 9 Maths
Cross a rectangle corner to corner
Open →Diagonal of a cuboid
Class 9 Maths
The longest rod that fits in a box
Open →Area by Heron's formula
Class 9 Maths
Area from just the three sides
Open →Interior angle sum of a polygon
Class 8 Maths
Add up a polygon's inside angles
Open →Exterior angle of a regular polygon
Class 8 Maths
Share 360 among a polygon's corners
Open →Number of diagonals of a polygon
Class 8 Maths
Count the diagonals of a polygon
Open →Discriminant
Class 10 Maths
Test how many roots a quadratic has
Open →Sum of roots
Class 10 Maths
Sum of a quadratic's roots
Open →Punnett square (monohybrid cross)
Class 10 Biology
Cross two parents, predict the offspring
Open →Balancing chemical equations
Class 10 Chemistry
Slide coefficients until atoms balance
Open →Writing chemical formulae (valency)
Class 9 Chemistry
Criss-cross valencies into a formula
Open →Current from power
Class 10 Physics
Divide power by voltage for current
Open →Power (P = V^2 / R)
Class 10 Physics
Voltage squared over resistance
Open →Sine ratio
Class 10 Maths
Opposite over hypotenuse
Open →Cosine ratio
Class 10 Maths
Adjacent over hypotenuse
Open →Tangent ratio
Class 10 Maths
Opposite over adjacent
Open →Area of an equilateral triangle
Class 9 Maths
Area of an equilateral triangle
Open →Curved surface area of a cylinder
Class 9 Maths
Wrap only the curved side
Open →Loss percentage
Class 8 Maths
Sell below cost, find the loss %
Open →Amount with simple interest
Class 8 Maths
Principal plus its simple interest
Open →Distance formula
Class 10 Maths
Straight distance between two points
Open →States of matter
Class 9 Chemistry
Heat particles solid → liquid → gas
Open →Parts of a plant cell
Class 8 Biology
Tap a cell part to see its job
Open →Diagonal of a cube
Class 9 Maths
Longest diagonal through a cube
Open →Total surface area of a hemisphere
Class 9 Maths
Dome plus its flat circle
Open →Sum of first n natural numbers
Class 10 Maths
Add 1 + 2 + ... + n instantly
Open →Range of data
Class 9 Maths
Spread from smallest to largest
Open →Class mark
Class 9 Maths
Midpoint of a class interval
Open →Selling price from profit percent
Class 8 Maths
Mark up cost by a profit %
Open →Perimeter of a sector
Class 10 Maths
Two radii plus the curved arc
Open →Circumference from diameter
Class 8 Maths
Circumference straight from diameter
Open →Power (P = F x v)
Class 9 Physics
Force times velocity gives power
Open →Percentage of a number
Class 8 Maths
Find a percentage of a number
Open →Series and parallel circuits
Class 10 Physics
Break a bulb in series vs parallel
Open →Symbols of elements
Class 9 Chemistry
Match each element to its symbol
Open →Free fall (velocity)
Class 9 Physics
Drop from a height, hit this speed
Open →Free fall (time)
Class 9 Physics
How long a drop takes
Open →Free fall (distance)
Class 9 Physics
Distance fallen in a given time
Open →Complement of an event
Class 10 Maths
Chance an event does NOT happen
Open →Product of roots
Class 10 Maths
Product of a quadratic's roots
Open →Exterior angle theorem
Class 9 Maths
Exterior angle = sum of remote interiors
Open →Complementary angles
Class 10 Maths
What adds to 90 degrees
Open →Supplementary angles
Class 9 Maths
What adds to 180 degrees
Open →Perimeter of a semicircle
Class 10 Maths
Curved half plus the diameter
Open →Area of a semicircle
Class 10 Maths
Half the area of a circle
Open →Turning effect (moments)
Class 9 Physics
Balance the see-saw with moments
Open →Reflex arc
Class 10 Biology
Step through a reflex, stimulus to action
Open →Buoyant force (upthrust)
Class 9 Physics
Displace liquid, feel the upthrust
Open →Relative density
Class 9 Physics
Compare a density to water's
Open →Power in lifting a load
Class 9 Physics
Lift a load, faster needs more power
Open →Cosecant ratio
Class 10 Maths
Hypotenuse over opposite
Open →Secant ratio
Class 10 Maths
Hypotenuse over adjacent
Open →Cotangent ratio
Class 10 Maths
Adjacent over opposite
Open →Height from angle of elevation
Class 10 Maths
Height from an angle of elevation
Open →Area of a quadrant
Class 10 Maths
A quarter of a circle's area
Open →Interior angle of a regular polygon
Class 8 Maths
One inside angle of a regular polygon
Open →Sum of first n odd numbers
Class 10 Maths
Add the first n odd numbers
Open →Sum of first n even numbers
Class 10 Maths
Add the first n even numbers
Open →Quadratic formula (a root)
Class 10 Maths
Larger root of a quadratic
Open →LCM from HCF
Class 10 Maths
LCM from the product and HCF
Open →Depreciation
Class 8 Maths
Value drops by a % each year
Open →Cost price from selling price
Class 8 Maths
Work back to the cost price
Open →Downstream speed
Class 8 Maths
Row with the current
Open →Upstream speed
Class 8 Maths
Row against the current
Open →Average speed for a round trip
Class 8 Maths
Average speed there and back
Open →Sales tax / GST
Class 8 Maths
Tax added on a price
Open →Area of a ring (annulus)
Class 10 Maths
Area of a ring between two circles
Open →Edge of a cube from volume
Class 9 Maths
Edge back from the volume
Open →Radius from area
Class 10 Maths
Radius back from a circle's area
Open →Side from area of a square
Class 8 Maths
Side back from a square's area
Open →Height of a triangle from area
Class 9 Maths
Height back from area and base
Open →Rate from simple interest
Class 8 Maths
Rate back from the interest
Open →Time from simple interest
Class 8 Maths
Time back from the interest
Open →Principal from simple interest
Class 8 Maths
Principal back from the interest
Open →Mean proportional
Class 10 Maths
Geometric mean of two numbers
Open →Fourth proportional
Class 8 Maths
Complete the proportion a : b = c : ?
Open →Marked price from selling price
Class 8 Maths
Marked price back from the sale price
Open →Chambers of the human heart
Class 10 Biology
Tap a heart chamber to see its job
Open →Equation of a line (y = mx + c)
Class 9 Maths
Read y off a straight line
Open →Average term of an AP
Class 10 Maths
Average of first and last term
Open →Number of terms in an AP
Class 10 Maths
How many terms in an AP
Open →Midpoint of two points
Class 10 Maths
x-coordinate of a midpoint
Open →Empirical mode
Class 10 Maths
Estimate the mode from mean & median
Open →Length of a shadow
Class 10 Maths
Shadow from height and sun angle
Open →Train crossing a pole
Class 8 Maths
Speed to cross a pole
Open →Time and work
Class 8 Maths
More workers, fewer days
Open →Dividing in a ratio
Class 8 Maths
Split a total in a ratio
Open →Unitary method
Class 8 Maths
Cost of a single item
Open →Your progress — Foundation - Class 8 to 10
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Showing 24 questions for Class 10. Tap a card to reveal the answer.
PhysicsElectricityeasyState Ohm's law and define electrical resistance.
Reveal answer ↓
What it is
For a conductor at steady temperature, voltage = current x resistance (V = IR).
I = V / R = 6 / 3 = 2.00 A
Answer
Ohm's law states that, at constant temperature, the current I through a conductor is directly proportional to the potential difference V across it, so V = IR. Resistance R is the property of a conductor that opposes the flow of current; it is the ratio of potential difference to current, R = V/I, measured in ohm.
V = IR ; R = V/I
- •V is proportional to I at constant temperature
- •V = IR
- •R = V/I, unit ohm
- •Resistance opposes current flow
Why learn this
It's the single most-used rule in all electrical and electronics engineering.
💡 Memory trick
V = IR - the 'VIR' triangle: cover the one you want to find.
PhysicsElectricitymediumA current of 2 A flows through a 5 ohm resistor. Find the potential difference across it and the power dissipated.
Reveal answer ↓
What it is
Electric power is the rate of using electrical energy: P = VI (also I^2 R or V^2 / R).
Answer
Using Ohm's law, V = IR = 2 x 5 = 10 V. Power dissipated P = VI = 10 x 2 = 20 W (equivalently P = I^2 R = 4 x 5 = 20 W).
V = IR ; P = VI = I^2 R = V^2 / R
- •V = IR = 10 V
- •P = VI = 20 W
- •Check: P = I^2 R = 20 W
Why learn this
It's what your electricity bill charges for and why a heater draws far more than a phone charger.
💡 Memory trick
P = VI. If you know current and resistance, use P = I^2 R ('I-squared-R heating').
PhysicsElectricitymediumHow is the total resistance calculated for resistors joined in series and in parallel?
Reveal answer ↓
What it is
In series, resistances add up; in parallel, the combined resistance is smaller than the smallest one.
Answer
In a series combination the resistors are joined end to end so the same current flows through each, and the total resistance is the sum: R = R1 + R2 + R3. In a parallel combination the resistors are connected between the same two points and share the current, so the reciprocals add: 1/R = 1/R1 + 1/R2 + 1/R3. As a result the total resistance in parallel is always less than the smallest individual resistance. Household circuits are wired in parallel so every appliance gets the full voltage.
Series: R = R1 + R2 + R3 ; Parallel: 1/R = 1/R1 + 1/R2 + 1/R3
- •Series: same current, R = R1 + R2 + R3
- •Parallel: same voltage, 1/R = 1/R1 + 1/R2 + ...
- •Parallel total is less than the smallest resistor
- •Homes are wired in parallel
Why learn this
Every real circuit - torches, homes, gadgets - combines resistors, so this decides how current and voltage are shared.
💡 Memory trick
Series = Sum (R1 + R2). Parallel = reciprocals add (1/R), so the total drops below the smallest.
PhysicsElectricityeasyTwo resistors of 10 ohm and 20 ohm are connected in series. Find the total resistance. Slide to explore.
Reveal answer ↓
What it is
Resistors joined end to end (in series) have a combined resistance equal to their sum.
Answer
In series, resistances add: R = R1 + R2 = 10 + 20 = 30 ohm. The total resistance in a series combination is always greater than the largest individual resistor.
R = R1 + R2
- •Series: R = R1 + R2
- •Same current flows through each
- •Total is greater than either resistor
Why learn this
It's how total resistance is worked out in real circuits and fairy lights.
💡 Memory trick
Series -> add them up: R = R1 + R2. Total beats either one.
PhysicsElectricityeasy30 C of charge flows past a point in 60 s. Find the current. Slide to explore.
Reveal answer ↓
What it is
Electric current is the rate of flow of electric charge through a conductor.
Answer
Current = charge / time = 30 / 60 = 0.5 ampere (A). Current tells us how much charge flows each second, so more charge in less time means a larger current.
I = Q / t
- •Current = charge / time
- •Unit: ampere (A)
- •1 A = 1 coulomb per second
Why learn this
It's the basic quantity every circuit, fuse and appliance rating is built on.
💡 Memory trick
I = charge / time. One ampere = one coulomb per second.
PhysicsElectricitymediumA current of 2 A flows through a 5 ohm resistor. Find the power dissipated. Slide to explore.
Reveal answer ↓
What it is
The heat power produced in a resistor depends on the square of the current and the resistance.
Answer
Power = I^2 x R = 2^2 x 5 = 4 x 5 = 20 watt (W). Because the current is squared, doubling the current to 4 A would give 4^2 x 5 = 80 W - four times the heat.
P = I^2 x R
- •P = I^2 x R
- •Unit: watt (W)
- •Double the current -> four times the power
Why learn this
It's why fuses, heaters and bulbs work, and why thick wires stay cool.
💡 Memory trick
P = I^2 x R. Double the current -> four times the heat.
PhysicsElectricitymediumTwo resistors of 10 ohm and 20 ohm are connected in parallel. Find the total resistance. Slide to explore.
Reveal answer ↓
What it is
Resistors connected across the same two points (in parallel) give a combined resistance smaller than any one of them.
Answer
For two resistors in parallel, R = (R1 x R2) / (R1 + R2) = (10 x 20) / (10 + 20) = 200 / 30 = 6.67 ohm. Notice the total is smaller than either resistor, because the current now has more than one path to flow through.
R = (R1 x R2) / (R1 + R2)
- •Parallel: R = (R1 x R2) / (R1 + R2)
- •Total resistance is less than the smallest resistor
- •Same voltage across each branch
Why learn this
Home wiring is in parallel, so each appliance gets the full voltage and can switch on independently.
💡 Memory trick
Parallel -> R = (R1 x R2) / (R1 + R2). Total is less than the smallest.
PhysicsElectricityeasyA current of 2 A flows for 30 s. How much charge passes? Slide to explore.
Reveal answer ↓
What it is
The charge that flows is the current multiplied by the time it flows for.
Answer
Charge = current x time = 2 x 30 = 60 coulomb (C). A larger current, or a longer time, delivers more charge past a point in the circuit.
Q = I x t
- •Charge Q = current x time
- •Unit: coulomb (C)
- •1 A for 1 s = 1 C
Why learn this
It connects current to the total charge delivered by a battery or wire.
💡 Memory trick
Q = I x t. One ampere for one second delivers one coulomb.
PhysicsElectricitymediumA 1000 W heater runs for 5 hours. How many units (kWh) does it use? Slide to explore.
Reveal answer ↓
What it is
The electrical energy used is the power of a device multiplied by the time it runs, often measured in kilowatt-hours (units).
Answer
Energy = power x time = 1000 W x 5 h = 5000 Wh = 5 kilowatt-hours (kWh), that is 5 units. One unit of electricity is one kilowatt-hour - a 1000 W appliance running for one hour.
energy (kWh) = power (W) x time (h) / 1000
- •Energy = power x time
- •1 unit = 1 kilowatt-hour (kWh)
- •1 kWh = a 1000 W device for 1 hour
Why learn this
It's exactly what your electricity meter counts and your bill charges for.
💡 Memory trick
Energy (kWh) = power (kW) x time (h). 1 unit = 1 kWh.
PhysicsElectricitymedium60 J of work moves 5 C of charge between two points. Find the potential difference. Slide to explore.
Reveal answer ↓
What it is
The potential difference (voltage) between two points is the work done to move each unit of charge between them.
Answer
Potential difference = work done / charge = 60 / 5 = 12 volt (V). Voltage measures the energy given to each coulomb of charge, so 1 V means 1 J of work per coulomb.
V = W / Q
- •V = work / charge
- •Unit: volt (V)
- •1 V = 1 joule per coulomb
Why learn this
It's the 'push' a battery gives, driving current through a circuit.
💡 Memory trick
V = W / Q. One volt is one joule per coulomb.
PhysicsElectricityeasyA voltage of 12 V drives a current of 2 A. Find the resistance. Slide to explore.
Reveal answer ↓
What it is
From Ohm's law, the resistance of a conductor is the voltage across it divided by the current through it.
Answer
Resistance = voltage / current = 12 / 2 = 6 ohm. This is Ohm's law V = IR rearranged as R = V / I; for a fixed voltage, a larger current means a smaller resistance.
R = V / I
- •R = V / I
- •Unit: ohm
- •Rearranged from V = IR
Why learn this
It's how the resistance of any component is measured in practice.
💡 Memory trick
R = V / I. Rearrange V = IR to get resistance.
PhysicsElectricitymediumFind the heat produced by a 2 A current in a 5 ohm resistor for 10 s. Slide to explore.
Reveal answer ↓
What it is
The heat produced in a resistor is the square of the current times the resistance times the time.
Answer
Heat H = I^2 x R x t = 2^2 x 5 x 10 = 4 x 5 x 10 = 200 joule (J). Because the current is squared, doubling it would produce four times as much heat.
H = I^2 R t
- •H = I^2 R t
- •Unit: joule (J)
- •Heat depends on the square of the current
Why learn this
It's the working principle of heaters, geysers, irons and fuses.
💡 Memory trick
H = I^2 R t. Current is squared, so it matters most.
PhysicsElectricityeasyA device runs at 12 V and draws 2 A. Find its power. Slide to explore.
Reveal answer ↓
What it is
Electric power is the product of the voltage across a device and the current through it.
Answer
Power = voltage x current = 12 x 2 = 24 watt (W). This is the rate at which the device converts electrical energy; combined with Ohm's law it also gives P = I^2 R and P = V^2 / R.
P = V x I
- •P = V x I
- •Unit: watt (W)
- •Also P = I^2 R = V^2 / R
Why learn this
It's the wattage on every bulb, motor and charger.
💡 Memory trick
P = V x I. Volts times amps gives watts.
PhysicsElectricityeasyA home uses 100 units at 6 rupees per unit. Find the bill. Slide the values to explore.
Reveal answer ↓
What it is
The cost of electricity is the number of units (kilowatt-hours) used multiplied by the rate per unit.
Answer
Cost = units x rate = 100 x 6 = 600 rupees. One unit is one kilowatt-hour, so using fewer units - by switching off idle appliances - directly reduces the bill.
cost = units x rate per unit
- •Cost = units x rate per unit
- •1 unit = 1 kilowatt-hour
- •Fewer units -> smaller bill
Why learn this
It's exactly how your monthly electricity bill is worked out.
💡 Memory trick
Cost = units x rate per unit.
PhysicsElectricityeasyA 1100 W appliance runs on 220 V. What current does it draw? Slide to explore.
Reveal answer ↓
What it is
The current a device draws is its power divided by the supply voltage.
Answer
Current = power / voltage = 1100 / 220 = 5 A. This comes from P = V x I rearranged as I = P / V, and it decides the fuse rating the appliance needs.
I = P / V
- •I = P / V
- •Rearranged from P = V x I
- •Sets the fuse and wire rating
Why learn this
It tells us the right fuse and wire thickness for an appliance.
💡 Memory trick
I = P / V, rearranged from P = V x I.
PhysicsElectricitymediumFind the power of a 484 ohm element on 220 V. Slide to explore.
Reveal answer ↓
What it is
The power dissipated in a resistor is the square of the voltage divided by the resistance.
Answer
Power = V^2 / R = 220^2 / 484 = 48400 / 484 = 100 W. This form comes from combining P = VI with Ohm's law V = IR, and shows that a smaller resistance draws more power at a fixed voltage.
P = V^2 / R
- •P = V^2 / R
- •From P = VI and V = IR
- •Smaller R -> more power
Why learn this
It's handy when the voltage and resistance are known but not the current.
💡 Memory trick
P = V^2 / R (from P = VI and V = IR).
PhysicsElectricitymediumWhat happens to the other bulb when one bulb fails, in series versus parallel? Flip the wiring and break a bulb to explore.
Reveal answer ↓
What it is
In a series circuit the components share one path, while in a parallel circuit each has its own path.
In series the same current flows through both bulbs, one after the other.
Answer
In a series circuit there is only one path for the current, so if one bulb breaks the circuit is open and both bulbs go out. In a parallel circuit each bulb sits on its own branch and gets the full voltage, so if one breaks the other keeps glowing. That is why household wiring is done in parallel and each appliance also gets the same voltage.
- •Series: one path, same current, one break stops all
- •Parallel: separate paths, same voltage, others keep working
- •Homes are wired in parallel
Why learn this
It's why homes are wired in parallel - one faulty appliance must not switch off the rest.
💡 Memory trick
Series = one path (one breaks, all stop). Parallel = separate paths (one breaks, others run).
PhysicsElectricityeasyDefine electric current and potential difference, and state their SI units.
Reveal answer ↓
What it is
Electric current is the rate of flow of charge; potential difference is the work done to move a unit charge between two points.
Answer
Electric current is the rate of flow of electric charge through a conductor, given by I = Q/t, where Q is the charge and t is the time; its SI unit is the ampere (A). Potential difference between two points is the work done to move a unit positive charge from one point to the other, given by V = W/Q; its SI unit is the volt (V). A current flows only when there is a potential difference across the conductor.
I = Q/t ; V = W/Q
- •Current I = Q/t, unit ampere (A)
- •Potential difference V = W/Q, unit volt (V)
- •1 ampere = 1 coulomb per second
- •Current needs a potential difference
Why learn this
They are the two most basic quantities in every electric circuit.
💡 Memory trick
Current I = Q/t (ampere). Potential difference V = W/Q (volt).
PhysicsElectricitymediumState Ohm's law. A 12 V battery drives a current of 3 A through a resistor. Find its resistance.
Reveal answer ↓
What it is
Ohm's law states that current through a conductor is directly proportional to the potential difference across it at constant temperature.
Answer
Ohm's law states that, at constant temperature, the current I flowing through a conductor is directly proportional to the potential difference V across its ends, so V = IR, where R is the resistance. Rearranging, R = V/I = 12/3 = 4 ohm. So the resistance of the resistor is 4 ohm.
V = IR
- •V is proportional to I (constant temperature)
- •V = IR
- •R = V/I = 12/3
- •R = 4 ohm
Why learn this
It is the fundamental relationship used to analyse circuits.
💡 Memory trick
V = IR. Cover the quantity you want in the V-I-R triangle.
PhysicsElectricitymediumOn what factors does the resistance of a conductor depend?
Reveal answer ↓
What it is
The resistance of a wire depends on its length, area of cross-section, material and temperature.
Answer
The resistance R of a conductor depends on four factors: it is directly proportional to its length L (a longer wire has more resistance); it is inversely proportional to its area of cross-section A (a thicker wire has less resistance); it depends on the nature of its material through a property called resistivity (rho); and it generally increases with temperature. These are combined in the relation R = rho L / A.
R = rho L / A
- •R is directly proportional to length L
- •R is inversely proportional to area A
- •Depends on material (resistivity rho)
- •R = rho L / A ; increases with temperature
Why learn this
It explains why long, thin wires resist current more than short, thick ones.
💡 Memory trick
R = rho L / A. Longer -> more R; thicker (more area) -> less R.
PhysicsElectricitymediumThree resistors of 2 ohm, 3 ohm and 5 ohm are connected in series. Find the total resistance.
Reveal answer ↓
What it is
In a series combination, the same current flows through all resistors and the total resistance is the sum of the individual resistances.
Answer
In a series combination, the total (equivalent) resistance is the sum of the individual resistances: Rs = R1 + R2 + R3 = 2 + 3 + 5 = 10 ohm. So the total resistance is 10 ohm. In series, the same current flows through each resistor, and the total voltage is shared among them.
Rs = R1 + R2 + R3 (series)
- •Series: same current in all resistors
- •Rs = R1 + R2 + R3
- •= 2 + 3 + 5 = 10 ohm
- •Total resistance increases
Why learn this
It is used when we want to increase the total resistance in a circuit.
💡 Memory trick
Series: just add them up. Rs = R1 + R2 + R3.
PhysicsElectricityhardTwo resistors of 6 ohm and 3 ohm are connected in parallel. Find the equivalent resistance.
Reveal answer ↓
What it is
In a parallel combination, the voltage is the same across each resistor and the reciprocal of the total resistance is the sum of the reciprocals.
Answer
In a parallel combination, 1/Rp = 1/R1 + 1/R2 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. So Rp = 2 ohm. The equivalent resistance (2 ohm) is smaller than the smallest individual resistance (3 ohm), which is always true for parallel combinations. In parallel, the voltage across each resistor is the same.
1/Rp = 1/R1 + 1/R2 (parallel)
- •Parallel: same voltage across each
- •1/Rp = 1/R1 + 1/R2
- •1/6 + 1/3 = 1/2 -> Rp = 2 ohm
- •Rp is smaller than the smallest resistor
Why learn this
It is how home appliances are wired so each works at the full supply voltage.
💡 Memory trick
Parallel: add the reciprocals. 1/Rp = 1/R1 + 1/R2. Total is smaller than the smallest.
PhysicsElectricitymediumState Joule's law of heating. Find the heat produced in a 10 ohm resistor carrying 2 A for 30 s.
Reveal answer ↓
What it is
When current flows through a resistor, heat is produced according to Joule's law of heating, H = I^2 R t.
Answer
Joule's law of heating states that the heat produced in a resistor is directly proportional to the square of the current (I^2), to the resistance (R) and to the time (t) for which the current flows: H = I^2 R t. Here H = 2^2 x 10 x 30 = 4 x 10 x 30 = 1200 J. So 1200 joules of heat is produced.
H = I^2 R t
- •H = I^2 R t (Joule's law)
- •Heat depends on current squared
- •H = 4 x 10 x 30
- •H = 1200 J
Why learn this
It is the working principle of heaters, geysers, irons and electric bulbs.
💡 Memory trick
H = I^2 R t. Heat depends on the square of the current.
PhysicsElectricitymediumAn electric bulb is rated 60 W, 240 V. Find the current it draws and its resistance.
Reveal answer ↓
What it is
Electric power is the rate of consuming electrical energy, P = VI = I^2 R = V^2/R; energy is charged in kilowatt-hours.
Answer
The current drawn is found from P = VI, so I = P/V = 60/240 = 0.25 A. The resistance is found from P = V^2/R, so R = V^2/P = 240^2/60 = 57600/60 = 960 ohm. So the bulb draws 0.25 A and has a resistance of 960 ohm.
P = VI = I^2 R = V^2/R
- •P = VI = I^2 R = V^2/R
- •I = P/V = 60/240 = 0.25 A
- •R = V^2/P = 57600/60 = 960 ohm
- •Energy unit: kilowatt-hour (kWh)
Why learn this
It determines the running cost of appliances on the electricity bill.
💡 Memory trick
P = VI. Energy (kWh) = power (kW) x time (h). 1 unit = 1 kWh.
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