Question

A cell of emf E and internal resistance r is connected to a load of resistance R. Find the maximum power transferred by the cell?
1. \(\frac{E^{2}}{4r}\)
2. \(\frac{E^{2}}{4R}\)
3. \(\frac{E^{2}}{2(r+R)}\)
4. All of the above

Answer 1

Correct Answer - Option 4 : All of the above

CONCEPT:

MAXIMUM POWER THEOREM:

• It states that the output power of a source of emf is maximum when external resistance in the circuit is equal to the internal resistance of the source.
• If emf of the battery is E, internal resistance r, and load resistance R, then maximum power transferred to the load is possible when 

⇒ R = r

• The maximum power P is given by 

\(⇒ P = \frac{E^{2}}{4r} = \frac{E^{2}}{4R} = \frac{E^{2}}{2(r+R)}\)

EXPLAINATION:

• From the above discussion, it is clear that the cell transfers maximum power when internal resistance is equal to the load resistance.
• The maximum power is given by options (1), (2), (3).
• Hence, the correct option is (4).