Question

A battery of emf E and internal resistance r is connected with an external resistance R as shown in figure. The battery will act as a constant voltage source if:

• A. r ,<< R
• B. r>> R
• C. r = R
• D. It will never act as a constant voltage source

Answer 1

The Correct Option is A

Given:
A battery of emf \( E \) and internal resistance \( r \) is connected in series with an external resistance \( R \).

Concept:
The voltage across the external resistance \( R \) is given by: \[ V = E - Ir \] where \( I = \frac{E}{R + r} \) So the voltage across \( R \) becomes: \[ V = E - \left( \frac{E}{R + r} \right) r = \frac{E R}{R + r} \] 

For the battery to act as a constant voltage source:
The voltage across the external resistance \( V \approx E \). This happens when the drop across internal resistance is negligible. \[ \text{This implies } r \ll R \] 

Therefore, the battery will act as a constant voltage source when:
r << R