Question

$AB$ and $CD$ are two uniform resistance wires of lengths $100cm$ and $80cm$, respectively. The connections are shown in the figure. The cell of emf $5V$ is ideal while the other cell of emf $E$ has an internal resistance of $2\Omega$. A length of $20cm$ of wire $CD$ is balanced by $40cm$ of wire $AB$. Find the emf $E$ (in volt), if the reading of the ideal ammeter is $2A$. The other connecting wires have negligible resistance.

Answer 1

Answer: 12

Potential difference across wire $AB=5V$
$\therefore$ Potential difference across $40cm$ of this wire
$=\frac{5}{100}\times 40=2V$
$\therefore$ Potential difference across $20cm$ of wire $CD$
$=2V$
$\therefore$ Potential difference across wire $CD$
$=\frac{2}{20}\times 80=8V$
Potential difference across $2\Omega$ resistor
$=2\times 2=4V$
$\therefore$ Emf of the cell $=12V$