The diagram above shows three resistors connected across a cell of e.m.f. 1.8 V and internal resistance r. Calculate :
The internal resistance r.
Topic: Current, resistance and circuits
Answer
Given: e.m.f. ε = 1.8 V, main current I = 0.3 A
external resistances: 4 Ω in series with the 1 Ω parallel combination
R_external = 4 + 1 = 5 Ω
For the whole circuit: ε = I (R_external + r) 1.8 = 0.3 × (5 + r) 1.8 ÷ 0.3 = 5 + r 6 = 5 + r r = 6 − 5 r = 1 Ω
Internal resistance of the cell, r = 1 Ω
The e.m.f. is shared between the outside of the circuit and the inside of the cell, so ε = I(R + r). Reduce the external network to one number first — here 5 Ω — then solve for r.
Do not confuse e.m.f. with terminal voltage. The e.m.f. of 1.8 V is what the cell would give with nothing connected; the terminal voltage is lower, here 0.3 × 5 = 1.5 V, and the missing 0.3 V is dropped inside the cell across r. Both views give r = 1 Ω, and checking one against the other is a good habit.