Question

A cell of constant e.m.f. is first connected to a resistance $R_{1}$ and then connected to a resistance $R_{2}.$ If power delivered in both cases is equal, then the internal resistance of the cell is

• A. $\sqrt{R_{1} R_{2}}$
• B. $\sqrt{\frac{R_{1}}{R_{2}}}$
• C. $\frac{R_{1} - R_{2}}{2}$
• D. $\frac{R_{1} + R_{2}}{2}$

Answer 1

Answer: (A)

A cell of constant $emf=E$ and internal
resistance $r$ is connected to $R_{1}$ then Power $P=\left(\frac{E}{R_{1} + r}\right)^{2}R_{1}\ldots ..\left(\right.1\left.\right)$
If cell is connected to $R_{2}$ then Power $P=\left(\frac{E}{R_{2} + r}\right)^{2}R_{2}\ldots .\left(\right.2\left.\right)$
If power in both case is same then by equation
$\left(\right.1\left.\right)$ and $\left(\right.2\left.\right)$ $\frac{R_{1}}{\left(R_{1} + r\right)^{2}}=\frac{R_{2}}{\left(R_{2} + r\right)^{2}}$
On solving $r=\sqrt{R_{1} R_{2}}$