Question

Two bulbs $A$ and $B$ rated $25W$, $220V$ and $100W$, $220V$, respectively, are connected in series across a $440V$ mains. As a result:

• A. $A$ will burn out.
• B. $B$ will burn out.
• C. Both $\left(1\right)$ and $\left(2\right)$ burn with same brightness.
• D. Neither $\left(1\right)$ or $\left(2\right)$ will glow.

Answer 1

The correct option is A $A$ will burn out.

Resistance of bulb $A=R_1=\frac{V^2}{P}$
$=\frac{220\times 220}{25}$
$R_1=1936\Omega$
Resistance of bulb $B=R_2=\frac{220\times 220}{100}=484\Omega$
Current through bulbs $=I=\frac{440}{R_1+R_2}=\frac{440}{2420}=\frac{2}{11}A$
P.d. across the bulb $A=V_1=I{R}_1=\frac{2}{11}\times 1936$
$V_1=I{R}_1=\frac{2}{11}\times 1936=352V$
It is much greater than its rated potential difference of $220V$
Therefore, bulb $A$ will burn out.
Potential difference across bulb $B=V_2=I{R}_2=\frac{2}{11}\times 484=88V$
Much less than this rated potential difference of $220V$
Therefore, bulb $B$ will not burn out