Question

A battery of emf V and internal resistance r is connected to N identical bulbs, all in parallel. Resistance of each bulb is R. It is observed that maximum cumulative power is dissipated in the bulbs if N = 10. Can we say that $r=\frac{R}{10}$

Answer 1

Yes, $r = \frac{R}{10}$.

Answer 2

1. Effective Resistance:
   For N bulbs in parallel, the effective resistance is

   $$R_{\text{parallel}}=\frac{R}{N}$$

2. Maximum Power Transfer:
   According to the maximum power transfer theorem, maximum power is delivered to the load when the load resistance equals the battery's internal resistance.

   $$\frac{R}{N}=r$$

3. Given Condition:
   It is observed that maximum power is dissipated when $N=10$. Substituting, we get

   $$\frac{R}{10}=r \quad \Rightarrow \quad r=\frac{R}{10}$$