question_answer

In the circuit shown, if the resistance\[5\,\Omega \]develops a heat of 42 J per  second, heat developed in 20 must be about (in\[J{{s}^{-1}}\])

A)  25                         

B)         20

C)  30                         

D)         35

E)  40

Correct Answer: C

Solution :

The simplified circuit is shown below: From figure, \[15{{I}_{1}}=5{{I}_{2}}\]or \[{{I}_{2}}=\frac{15{{I}_{1}}}{5}=3{{I}_{1}}\] \[\therefore \]  \[I={{I}_{1}}+{{I}_{2}}=\frac{{{I}_{2}}}{3}+{{I}_{2}}=\frac{4{{I}_{2}}}{3}\]     ...(i) But         \[I_{2}^{2}\times 5=42\] \[I_{2}^{2}=\frac{42}{5}=8.4\] Putting value of\[{{I}_{2}}\]in Eq. (i), we get \[I=\frac{4}{3}\times \sqrt{8.4}\] Therefore, heat dissipated across \[2\,\Omega \]                 \[={{I}^{2}}\times 2\]                 \[=\frac{16}{9}\times 8.4\times 2\]                 \[\approx 30\,J{{s}^{-1}}\]