Question

A cell of constant emf is first connected to a resistance \(R_1\) and then to \(R_2\). If power delivered in both cases are same, then the internal resistance of the cell is:

• A. \(\sqrt{R_1 R_2}\)
• B. \(\frac{R_1}{R_2}\)
• C. \(\frac{R_1 + R_2}{2}\)
• D. \(\frac{R_1 - R_2}{2}\)

Hint:

In power calculation problems, use the equivalent resistance formula for the specific configuration and equate powers to solve for unknowns.

Answer 1

The Correct Option is C

For the power delivered to the load resistor in each case, we use the power formula: \[ P = \frac{V^2}{R_{\text{total}}} \] If the power is the same for both resistors, we equate the powers for both configurations: \[ \frac{V^2}{R_1 + r} = \frac{V^2}{R_2 + r} \] Solving this equation gives the internal resistance \(r = \frac{R_1 + R_2}{2}\).