First slide

Cell

Question

Two identical cells send the same current in $2 Ω$ resistance, whether connected in series or in parallel. The internal resistance of the cell should be

Moderate

A

$1 Ω$
B

$2 Ω$
C

$\frac{1}{2} Ω$
D

$2.5 Ω$

Solution

In series, $i_{1} = \frac{2 E}{2 + 2 r}$
In parallel, $i_{2} = \frac{E}{2 + \frac{r}{2}} = \frac{2 E}{4 + r}$
$Since i_{1} = i_{2} \Rightarrow \frac{2 E}{4 + r} = \frac{2 E}{2 + 2 r} \Rightarrow r = 2 Ω$

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