Question

A cell supplies currents of 1 A and 0.5 A through resistors of 2.5 \( \Omega \) and 10 \( \Omega \), respectively. The internal resistance of the cell is:

• A. 2 \( \Omega \)
• B. 3 \( \Omega \)
• C. 4 \( \Omega \)
• D. 5 \( \Omega \)

Hint:

Apply \( E = I(R + r) \) for internal resistance with multiple circuits.

Answer 1

The Correct Option is D

Let emf of cell be \( E \), internal resistance \( r \).
Using \( E = IR + Ir \) for both circuits: \[ E = 1 \cdot (2.5 + r) = 0.5 \cdot (10 + r) \Rightarrow 2.5 + r = 5 + 0.5r \Rightarrow 0.5r = 2.5 \Rightarrow r = 5\, \Omega \]