question_answer

The wiring of a house has resistance \[6\,\Omega .\] 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  [MNR 1998]

A)            Nil 

B)            23 V

C)            32 V                                         

D)            12 V

Correct Answer: B

Solution :

                   \[{{R}_{Bulb}}=\frac{{{220}^{2}}}{100}=484\,\,\Omega \], \[{{R}_{Geyser}}=\frac{{{220}^{2}}}{1000}=48.4\,\,\Omega \]                    (i) When only bulb is ON, \[{{V}_{Bulb}}=\frac{220\times 484}{490}=217.4\,V\] (ii) When geyser is also switched ON, equivalent resistance of bulb and geyser is \[R=\frac{484\times 48.4}{484+48.4}=44\,\Omega \] Voltage across the bulb \[{{V}_{Bulb}}=\frac{220\times 44}{50}=193.6\,V\]            Hence the potential drop is \[217.4-193.6=23.8\,\,V\]