Question

Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance 1.5 \(\Omega\). Find the value of internal resistance of each cell.

• A. 1 \(\Omega\)
• B. 0.5 \(\Omega\)
• C. zero
• D. 1.5 \(\Omega\)

Hint:

When series and parallel combinations give the same current, internal resistance equals external resistance: \(r = R\).

Answer 1

The Correct Option is D

Step 1: Basic Principle
For two identical cells (emf \(E\), internal resistance \(r\)), current in series: \(I_s = \dfrac{2E}{2r+R}\); current in parallel: \(I_p = \dfrac{E}{r/2 + R}\).
Step 2: Solution Procedure:
Setting \(I_s = I_p\): \[ \frac{2E}{2r + R} = \frac{E}{r/2 + R} \] \[ 2(r/2 + R) = 2r + R \] \[ r + 2R = 2r + R \] \[ R = r \] So \(r = R = 1.5\ \Omega\).
Step 3: Required Answer:
The internal resistance of each cell is 1.5 \(\Omega\).