Question

The wiring of a house has resistance $6\Omega .$ $A100W$ bulb is glowing. If a geyser of $1000W$ is switched on, the change in potential drop across the bulb is nearly

• A. $12V$
• B. $32V$
• C. $23V$
• D. Nil

Answer 1

The correct option is C $23V$

Rating of the house $=220V$
We know that $R=\frac{V^2}{P}$
For bulb, $V=220V,R=100\Omega$ and for geyser
$V=220V,R=1000\Omega$
$R_{Bulb}=\frac{{220}^2}{100}=484\Omega$
$R_{Geyser}=\frac{{220}^2}{1000}=48.4\Omega$
When only bulb in ON, $V_{Bulb}=\frac{220\times 484}{490}=217.4V$
When geyser is also switched ON, equivalent resistance of bulb and geyser is
$R=\frac{484\times 484}{484+484}=44\Omega$
Voltage across the bulb $V_{Bulb}=\frac{220\times 44}{50}=193.6V$
Hence the potential drop is $217.4V-193.6V=23.8V$
Hence, option $\left(b\right)$ is correct.