question_answer

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers \[{{P}_{1}}\]and \[{{P}_{2}}\]respectively, then [JEE Main Online Paper Held On 12-Jan-2019 Morning]

A) \[{{P}_{1}}=9W,{{P}_{2}}=16W\]                 

B) \[{{P}_{1}}=16\,W,{{P}_{2}}=4W\]

C) \[{{P}_{1}}=4\,W,{{P}_{2}}=16W\]               

D) \[{{P}_{1}}=16\,W,{{P}_{2}}=9W\]

Correct Answer: B

Solution :

Resistance across 25 W bulb \[{{R}_{1}}=\frac{{{V}^{2}}}{{{P}_{1}}}=\frac{220\times 220}{25}=1936\Omega \] Resistance across 100 W bulb \[{{R}_{2}}=\frac{{{V}^{2}}}{{{P}_{2}}}=\frac{220\times 220}{100}=484\Omega \] Total Resistance \[{{R}_{1}}+{{R}_{2}}=2420\Omega \] Total current \[I=\frac{V}{R}=\frac{220}{2420}=0.09A\] Power consumed by 25 W bulb \[{{I}^{2}}{{R}_{1}}=0.09\times 0.09\times 1936\cong 16W\] Power consumed by 100 W bulb \[{{I}^{2}}{{R}_{2}}=0.09\times 0.09\times 484\cong 4W\]