Question

A cell supplied a current of $0.9$A through a $2\Omega$ resistor and current of $0.3$A through $7\Omega$ resistor. What is the internal resistance of cell?

• A. $0.5\Omega$
• B. $1.0\Omega$
• C. $1.2\Omega$
• D. $2.0\Omega$

Answer 1

The correct option is A $0.5\Omega$

According to Ohm's law $V=IR$

Here also, $I$ = $\frac{V}{R+r}$, where $V$ potential of battery $R$ is external resistance and $r$ is internal resistance of the battery.

Given, for $R$= $2\Omega$, $I$ = $0.9A$

Using, $V=IR+Ir$

$\Rightarrow V=1.8+0.9r$ $....eq.1$

And, for $R$= $7\Omega$, $I$ = $0.3A$

Using, $V=IR+Ir$ again

$\Rightarrow V=2.1+0.3r$ $....eq.2$

From $eq.1$ and $eq.2$

1.8+ 0.9r = 2.1+ 0.3r

$\Rightarrow$ 0.6r = 0.3

$\Rightarrow$ r =$0.5\Omega$.

So, Internal resistance of the cell is $0.5\Omega$.

Therefore, A is correct option.