Cell Terminal Voltage and Internal Resistance Graph
For a cell of emf E and approximately constant internal resistance r delivering current I, terminal voltage is V = E - Ir, so a plot of V against I is a straight line with intercept E and slope -r.
Why this shows up in the exam
Battery load testing · Finding cell emf from an intercept · Finding internal resistance from a V-I graph
Learn the idea
A discharging cell's terminal voltage falls linearly with current because of its internal resistance. The cell supplies emf, but part of that energy per charge is lost inside the cell as current crosses its internal resistance; the graph intercept gives emf and the downward slope gives that resistance.
🧠 Memory hook: Intercept is emf; downward slope magnitude is internal resistance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V = E - Ir — terminal voltage of a discharging cell
- E = V at I=0; r = -dV/dI — graphical extraction of emf and internal resistance
How to approach it
- 1Identify graph axes and units
- 2Read the zero-current intercept
- 3Use the magnitude of Delta V/Delta I for r
Common slip-ups that cost marks
- •Taking the loaded terminal voltage as emf
- •Using slope I/V instead of V/I
- •Assigning a negative physical resistance because the graph slopes down
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In a meter bridge, resistance 2 ohm is in the left gap and balance occurs at 40 cm from the left end. Find the right-gap resistance.
More from Experimental Skills
Vernier Least Count and Direct Reading
For a direct vernier, the least count is one main-scale division minus one vernier-scale division, and the observed reading is the main-scale reading plus the coinciding vernier division multiplied by that least count.
Vernier Zero Error and Correction
Vernier zero error is the signed reading shown when the jaws are in true contact; the zero correction is its negative, so the corrected measurement equals the observed measurement minus the signed zero error.
Screw-Gauge Pitch and Least Count
The pitch is the axial distance moved by the spindle per complete rotation, and the screw-gauge least count is the pitch divided by the number of equal divisions on the circular scale.
Screw-Gauge Reading and Zero Correction
The observed screw-gauge reading is the pitch-scale reading plus the circular-scale reading times the least count, and the corrected value is obtained by subtracting the signed zero error measured with the studs in contact.
Resolution and Propagation of Measurement Uncertainty
For independent small limiting uncertainties, the maximum fractional uncertainty of a product of powers Q = product(x_i raised to n_i) is the sum of |n_i| times Delta x_i/x_i; a directly read scale cannot justify resolution finer than its least count.
Stokes-Law Viscosity by Terminal Speed
For a small sphere moving slowly through an effectively unbounded Newtonian liquid, Stokes drag is 6 pi eta R v; balancing drag with weight minus buoyancy gives terminal speed proportional to R squared and inversely proportional to viscosity.