A cell of emf $ε$ and internal resistance r drives a current i through an external resistance R.
a) The cell supplies εi power
b) Heat is produced in R at the rate $ε$ i
c) Heat is produced in R at the rate $εi (\frac{R}{R + r})$
d) Heat is produced in the cell at the rate $ε$ $i (\frac{r}{R + r})$

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a, c & d are only true

b & d are only true

all are true

a & b are only true

answer is C.

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Detailed Solution

Given current in circuit is i.

Power supplied by the cell will be

P = $εi$

we know, $i = \frac{ε}{r + R}$

Potential difference across R is

V = i R

$V = (\frac{ε}{r + R}) R$

Rate of heat production in R is

$\frac{dH}{dt} = iV = i (\frac{ε}{r + R}) R$

Rate of heat production in r or cell is

$\frac{dH}{dt} = iV = i (\frac{ε}{r + R}) r$

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