Question

In a circuit there is a battery with internal resistance \( r \) and Emf \( E \), which is connected to external load resistance \( R \) as shown. Find the value of \( R \) so that maximum power dissipates across \( R \).

• A. \( R = r \)
• B. \( R = \frac{r}{2} \)
• C. \( R = \sqrt{2}r \)
• D. \( R = 2r \)

Hint:

For maximum power dissipation, the load resistance should always equal the internal resistance of the source.

Answer 1

The Correct Option is A

Step 1: Maximum Power Transfer Theorem.
According to the Maximum Power Transfer Theorem, maximum power is dissipated across the load resistance \( R \) when the load resistance is equal to the internal resistance \( r \) of the source.
Step 2: Apply the theorem.
For maximum power dissipation across \( R \), the condition is: \[ R = r \] Conclusion.
Thus, the correct value of \( R \) is \( r \), as stated in option (1).