When a resistance ' $R_{1}{ }^{\prime}$ is connected across the terminal of a cell of e.m.f. ' $\mathrm{E}_{1}$ ' the current is ' $\mathrm{I}_{1}$ '. When the resistance is changed to $\mathrm{R}_{2}$ ' the current is ' $I_{2}$ '. The internal resistance of the cell isA. $\frac{I_{1} R_{2}+I_{2} R_{1}}{I_{1}+I_{2}}$B. $\frac{I_{2} R_{2}+I_{1} R_{1}}{I_{1}+I_{2}}$C. $\frac{I_{2} R_{2}-I_{1} R_{1}}{I_{1}-I_{2}}$D. $\frac{I_{1} R_{2}-I_{2} R_{1}}{I_{1}-I_{2}}$

Home » When a resistance ‘ is connected across the terminal of a cell of e.m.f. ‘ ‘ the current is ‘ ‘. When the resistance is changed to ‘ the current is ‘ ‘. The internal resistance of the cell isA. B. C. D.

When a resistance ‘ $R_{1}{ }^{\prime}$ is connected across the terminal of a cell of e.m.f. ‘ $\mathrm{E}_{1}$ ‘ the current is ‘ $\mathrm{I}_{1}$ ‘. When the resistance is changed to $\mathrm{R}_{2}$ ‘ the current is ‘ $I_{2}$ ‘. The internal resistance of the cell is
A. $\frac{I_{1} R_{2}+I_{2} R_{1}}{I_{1}+I_{2}}$
B. $\frac{I_{2} R_{2}+I_{1} R_{1}}{I_{1}+I_{2}}$
C. $\frac{I_{2} R_{2}-I_{1} R_{1}}{I_{1}-I_{2}}$
D. $\frac{I_{1} R_{2}-I_{2} R_{1}}{I_{1}-I_{2}}$

Physics

When a resistance ‘ $R_{1}{ }^{\prime}$ is connected across the terminal of a cell of e.m.f. ‘ $\mathrm{E}_{1}$ ‘ the current is ‘ $\mathrm{I}_{1}$ ‘. When the resistance is changed to $\mathrm{R}_{2}$ ‘ the current is ‘ $I_{2}$ ‘. The internal resistance of the cell is
A. $\frac{I_{1} R_{2}+I_{2} R_{1}}{I_{1}+I_{2}}$
B. $\frac{I_{2} R_{2}+I_{1} R_{1}}{I_{1}+I_{2}}$
C. $\frac{I_{2} R_{2}-I_{1} R_{1}}{I_{1}-I_{2}}$
D. $\frac{I_{1} R_{2}-I_{2} R_{1}}{I_{1}-I_{2}}$

Correct answer is C.

$\begin{array}{l} I_{1}=\frac{E}{r+R_{1}} \\ I_{2}=\frac{E}{r+R_{2}} \\ \frac{I_{1}}{I_{2}}=\frac{r+R_{2}}{r+R_{1}} \\ I_{1} r+I_{1} R_{1}=I_{2} r+I_{2} R_{2} \\ r\left(I_{1}-I_{2}\right)=I_{2} R_{2}-I_{1} R_{1} \\ r=\frac{I_{2} R_{2}-I_{1} R_{1}}{I_{1}-I_{2}} \end{array}$

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