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Resistance and Resistors

When a resist...

Question

When a resistance $R_{1}$ is connected across the terminal of a cell, the current is $I_{1}$ , when the resistance is changed to $R_{2}$ , the current is $I_{2}$ . The internal resistance of the cell is:

$\frac{I_{1} R_{1} + I_{2} R_{2}}{I_{1} + I_{2}}$

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$\frac{I_{1} R_{2} + I_{2} R_{1}}{I_{1} + I_{2}}$

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$\frac{I_{1} R_{2} + I_{2} R_{1}}{I_{1} - I_{2}}$

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$\frac{I_{2} R_{2} - I_{1} R_{1}}{I_{1} - I_{2}}$

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Solution

The correct option is D
$\frac{I_{2} R_{2} - I_{1} R_{1}}{I_{1} - I_{2}}$

$I_{1} = \frac{E}{r + R_{1}} I_{2} = \frac{E}{r + R_{2}} \frac{I_{1}}{I_{2}} = \frac{r + R_{2}}{r + R_{1}} I_{1} r + I_{1} R_{1} = I_{2} r + I_{2} R_{2} r (I_{1} - I_{2}) = I_{2} R_{2} - I_{1} R_{1} r = \frac{I_{2} R_{2} - I_{1} R_{1}}{I_{1} - I_{2}}$

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When a resistance R1 is connected across the terminal of a cell, the current is I1, when the resistance is changed to R2, the current is I2. The internal resistance of the cell is:

The correct option is D I2R2−I1R1I1−I2 I1=Er+R1I2=Er+R2I1I2=r+R2r+R1I1r+I1R1=I2r+I2R2r(I1−I2)=I2R2−I1R1r=I2R2−I1R1I1−I2

When a resistance $R_{1}$ is connected across the terminal of a cell, the current is $I_{1}$ , when the resistance is changed to $R_{2}$ , the current is $I_{2}$ . The internal resistance of the cell is: