The wiring of a house has resistance 6  Ω. A 100 W bulb is glowing. If a geyser of 1000 W is switched on, the change in potential drop across the bulb is nearly (Supply voltage is 220 V)

# The wiring of a house has resistance $6\text{\hspace{0.17em}\hspace{0.17em}}\Omega .$ A 100 W bulb is glowing. If a geyser of 1000 W is switched on, the change in potential drop across the bulb is nearly (Supply voltage is 220 V)

1. A

nil

2. B

23 V

3. C

32 V

4. D

12 V

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### Solution:

${\mathrm{R}}_{\mathrm{Bulb}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{{220}^{2}}{100}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}48.4\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{\Omega }$

(i) When only bulb is ON,  ${\mathrm{V}}_{\mathrm{Bulb}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{220\text{\hspace{0.17em}}×\text{\hspace{0.17em}}484}{490}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}217.4\text{\hspace{0.17em}}\mathrm{V}$

(ii) When geyser is also switched ON, equivalent resistance of bulb and geyser is $\mathrm{R}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{484\text{\hspace{0.17em}}×\text{\hspace{0.17em}}48.4}{484+48.4}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}44\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{\Omega }$

Voltage across the bulb, ${\mathrm{V}}_{\mathrm{Bulb}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{220\text{\hspace{0.17em}}×\text{\hspace{0.17em}}44}{50}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}193.6\text{\hspace{0.17em}}\mathrm{V}$

Hence, the potential drop is $217.4-193.6=23.8\text{\hspace{0.17em}\hspace{0.17em}}V$  Register to Get Free Mock Test and Study Material

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