Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Every light you switch on is Ohm's law quietly at work.”
A frequent error is adding parallel resistances directly instead of their reciprocals. In reality, in series the current is the same and resistances add; in parallel the voltage is the same and 1/R values add.
Memory trick: parallel resistance is always less than the smallest branch.
“Every light you switch on is Ohm's law quietly at work.”
EMF is the battery's full push; terminal voltage is what's left after the internal resistance drops some of it.
Memory trick: terminal V = EMF − I·r, so it drops under load.
“Every light you switch on is Ohm's law quietly at work.”
A frequent error is assuming terminal voltage equals EMF even when current flows. In reality, EMF is the battery's full push; terminal voltage is what's left after the internal resistance drops some of it.
Memory trick: terminal V = EMF − I·r, so it drops under load.
“Every light you switch on is Ohm's law quietly at work.”
Ohm's law relating voltage, current and resistance. Use it when ohmic conductor at fixed temperature.
V = IR
“Every light you switch on is Ohm's law quietly at work.”
Resistance from resistivity, length and area. Use it when uniform conductor.
R = ρL/A
“Every light you switch on is Ohm's law quietly at work.”
Electrical power dissipated. Use it when any resistor.
P = VI = I²R = V²/R
“Every light you switch on is Ohm's law quietly at work.”
Combining resistors in parallel. Use it when parallel connection.
1/R = 1/R₁ + 1/R₂
“Every light you switch on is Ohm's law quietly at work.”
In series components share the current and split the voltage; in parallel they share the voltage and split the current.
“Every light you switch on is Ohm's law quietly at work.”
Resistance (Ω) depends on the object's size and shape; resistivity (Ω·m) is an intrinsic material property.
“Every light you switch on is Ohm's law quietly at work.”
You must add reciprocals — the parallel total is smaller than any single resistor.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
F = qvB·sinθ, always perpendicular to the velocity, so it changes direction but not speed.
Memory trick: a magnetic force does zero work — it only bends the path.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
A frequent error is thinking the magnetic force can speed a charge up. In reality, F = qvB·sinθ, always perpendicular to the velocity, so it changes direction but not speed.
Memory trick: a magnetic force does zero work — it only bends the path.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
A changing magnetic flux induces an EMF, EMF = −dΦ/dt.
Memory trick: only a CHANGE in flux — move the magnet or change the area/field — induces current.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
A frequent error is expecting a steady (unchanging) magnetic field to induce an EMF. In reality, a changing magnetic flux induces an EMF, EMF = −dΦ/dt.
Memory trick: only a CHANGE in flux — move the magnet or change the area/field — induces current.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
A frequent error is getting the direction of induced current backwards. In reality, the induced current always opposes the change that produced it, ensuring energy conservation.
Memory trick: nature resists change: the induced current fights the flux change.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Φ = B·A·cosθ — the amount of field passing through a loop.
Memory trick: flux is maximum when the field is perpendicular to the loop's plane.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
A frequent error is ignoring the angle between the field and the loop's normal. In reality, Φ = B·A·cosθ — the amount of field passing through a loop.
Memory trick: flux is maximum when the field is perpendicular to the loop's plane.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Force on a charge moving through a magnetic field. Use it when charge q with velocity v.
F = qvB sinθ
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Force on a current-carrying wire in a field. Use it when straight wire of length L.
F = BIL sinθ
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Faraday's law of electromagnetic induction. Use it when flux is changing with time.
EMF = −dΦ/dt
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Magnetic flux through a flat loop. Use it when uniform field over area A.
Φ = BA cosθ
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
The electric force acts along the field and can do work; the magnetic force acts perpendicular to velocity and does no work.
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Faraday's law gives the SIZE of the induced EMF; Lenz's law gives its DIRECTION (opposing the change).
“Every power plant on Earth spins a magnet to make your electricity — Faraday's idea, scaled up.”
Alternating current periodically reverses direction (mains supply); direct current flows one way (batteries).