Question

Forty electric bulbs are connected in series across $220V$ supply. After one bulb is fuse the remaining $39$ are connected again in series across the same potential. The illumination will be

• A. more with $40$ bulbs than with $39$ bulbs
• B. more with $39$ bulbs then with $40$ bulbs
• C. equal in both cases
• D. in ratio ${40}^2:{39}^2$

Answer 1

The correct option is B more with $39$ bulbs then with $40$ bulbs

Let resistance of each bulb $=R$

When forty bulbs are connected in series $I_1=\frac{220}{40R}$

When 39 bulbs are connected in series $I_2=\frac{220}{39R}$

Here $I_2>I_1$

As illumination depends upon power output, $I_2>I_1$ makes $I_2^{2}R>I_1^{2}R$ increasing brightness in second case.