Ohm's Law
Ohm's law is examined both as a statement and as a calculation tool. Expect questions on the V–I graph, on series and parallel behaviour, on internal resistance, and on identifying circuits where the law does not hold.
Statement and conditions
At constant temperature, the current through a metallic conductor is directly proportional to the potential difference across it: V = IR, with V in volts, I in amperes and R in ohms. The V–I graph is a straight line through the origin whose slope equals R.
The law holds only for ohmic conductors at constant temperature. Filament lamps, thermistors, diodes and electrolytes are non-ohmic: resistance changes with current, temperature or polarity.
Circuit consequences
- Series: same current everywhere; p.d. divides in proportion to resistance; R_s = R1 + R2 + R3.
- Parallel: same p.d. across each branch; current divides inversely with resistance; 1/R_p = 1/R1 + 1/R2.
- Real source: with internal resistance r, the terminal voltage on load is V = E − I r, and the short-circuit current is E/r.
Worked example
A 230 V, 60 W filament lamp. Current I = P/V = 60/230 = 0.261 A. Resistance R = V²/P = 52900/60 = 881.7 Ω. Check: V/I = 230/0.261 = 881 Ω, which agrees. This is the hot, operating resistance, not the cold value measured with a multimeter.
Traps
- Applying V = IR to a whole circuit while ignoring internal resistance.
- Assuming R stays fixed when the conductor heats.
- Swapping the current-divider and voltage-divider formulas.
- Giving the slope of the V–I graph the unit A/V instead of ohms.