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Question
A cell of e.m.f. ε and internal resistance 𝔯 sends current 1.0 A when it is connected to an external resistance 1.9 Ω. But it sends current 0.5 A when it is connected to an external resistance 3.9 Ω. Calculate the values of ε and 𝔯.
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Solution
In first case
I = 1 A, R = 1.9 ohm
ε = I (R + r)
= 1(1.9 + r)
ε = 1.9 + r ...(1)
In second case
I = 0.5 A, R = 3.9 ohm
ε = I(R + r)
= 0.5 (3.9 + r)
ε = 1.95 + 0.5r ...(2)
From eq. (1) and (2),
1.9 + r = 1.95 + 0.5r
r = `0.05/0.5`
r = 0.1 ohm
Substituting value of r
ε = 1.9 + r
= 1.9 + 0.1
= 2 V
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