question_answer

In the circuit shown in figure, the heat produced in 5 ohm resistance is 10 calories per second. The heat produced in 4 resistance is                                                   [IIT 1981; UPSEAT 2002]

A)            1 cal / sec

B)            2 cal/sec

C)            3 cal / sec

D)            4 cal/sec

Correct Answer: B

Solution :

                   \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}=\frac{10}{5}=\frac{2}{1}\] Also heat produced per sec i.e. \[\frac{H}{t}=P={{i}^{2}}R\] Þ\[\frac{{{P}_{5}}}{{{P}_{4}}}={{\left( \frac{{{i}_{1}}}{{{i}_{2}}} \right)}^{2}}\times \frac{5}{4}={{\left( \frac{2}{1} \right)}^{2}}\times \frac{5}{4}=\frac{5}{1}\]Þ \[{{P}_{4}}=\frac{10}{5}=2\,cal/s\]