Question

A cell supplies a current of 0.9 A through a 2 Ω resistor and a current of 0.3 A through a 7 Ω resistor. Calculate the internal resistance of the cell.

Answer 1

Current from the cell, I₁ = 0.9 A

Resistor, R₁ = 2 Ω

Current from the cell, I₂ = 0.3 A

Resistor, R₂ 7 Ω

Internal resistance of the cell, r = ?

Current in the circuit I₁ = `ξ/("r" + "R"_1)`

ξ = I₁ (r + R₁) …… (1)

Current in the circuit, I₂ = `ξ/("r" + "R"_2)`

Equating equation (1) and (2),

I₁r + I₁R₁ = I₂R₂ + I₂r

(I₁ – I₂)r = I₂R₂ – I₁R₁

r = `("I"_2"R"_2 - "I"_1"R"_1)/("I"_1 - "I"_2)`

`= ((0.3 xx 7) - (0.9 xx 2))/(0.9 - 0.3)`

`= (2.1 - 1.8)/0.6`

`= 0.3/0.6`

r = 0.5 Ω.