Question

Two sources of equal emf are connected to a resistance \( R \). The internal resistance of the sources are \( r_1 \) and \( r_2 \), \( (r_1>r_2) \). If the potential difference across the source having internal resistance \( r_2 \) is zero, then

• A. \( R = \frac{r_2}{r_1 - r_2} \)
• B. \( R = \frac{r_1 + r_2}{r_1} \)
• C. \( R = \frac{r_1 r_2}{r_1 + r_2} \)
• D. \( R = r_2 - r_1 \)

Hint:

In problems involving internal resistance of sources, the total resistance in the circuit can be determined using the parallel resistance formula.

Answer 1

The Correct Option is C

In this case, when the potential difference across the second source becomes zero, it implies that the two internal resistances are balanced. The effective resistance is given by the formula \( R = \frac{r_1 r_2}{r_1 + r_2} \).