Question

A $25W$, $220V$ bulb and a $100W$, $220V$ bulb are connected in series across a $440V$ line. Select the correct answer from the options given below.

• A. Only $100W$ bulb will fuse.
• B. Only $25W$ bulb will fuse.
• C. Both bulbs will fuse.
• D. None of the bulb will fuse.

Answer 1

The correct option is B Only $25W$ bulb will fuse.

$P_1=\frac{V^2}{R_1}$

$R_1=\frac{{\left(220\right)}^2}{25}$

$P_2=\frac{V^2}{R_2}$

$R_2=\frac{{\left(220\right)}^2}{100}$

$\Rightarrow \frac{R_1}{R_2}=\frac{4}{1}$ P.D across bulb $\alpha$ Resistance of bulb

Let the P.D across bulb 2 be x

then across bulb 1 will be 4x

P.D. of 1 + P.D. of 2 $=$ 440

$\Rightarrow$ 5x $=$ 440

$\Rightarrow x=88$

$\Rightarrow$ P.D across bulb 1 $=$ 4 x x $=$ 352 which is > 220

$\Rightarrow$ bulb will fuse
P.D across bulb 2 $=$ x $=$ 88 < 220

$\Rightarrow$ bulb will glow

$\therefore$ Bulb 1 which is of 25 W will fuse.