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Series Combination of Cells

In the situat...

Question

In the situation shown, the potential difference across the cell of smaller e.m.f. is

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Solution

Equivalent resistance,
All the resistors are in series
$\Rightarrow R_{e q} = 1 + 2 + 1 = 4 Ω$
Equivalent voltage,
As both batteries are connected opposite
$\Rightarrow V_{e q} = 10 - 2 = 8 V$
So, current in the circuit
$V = I R$ (Ohm's law)
$8 = I \times 4$
$I = 2 A$
By KVL
$V_{A} - 2 + 2 \times 1 = V_{R}$
$V_{A} - V_{B} = 2 - 2 = 0$
Thus, potential difference across smaller cell is $V_{A} - V_{B} = O V$ .

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