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 $P={\left(\frac{E}{R_1+r}\right)}^2{R}_1\dots ..(1)$
If cell is connected to $R_2$ then Power $P={\left(\frac{E}{R_2+r}\right)}^2{R}_2\dots .(2)$
If power in both case is same then by equation
$(1)$ and $(2)$ $\frac{R_1}{{\left(R_1+r\right)}^2}=\frac{R_2}{{\left(R_2+r\right)}^2}$
On solving $r=\sqrt{R_1{R}_2}$