Question

In the circuit shown in the figure, the heat produced it is the 5 $\Omega$ resistor due to the current flowing through it is 10 calories per second. The heat generated in the 4 $\Omega$ resistor is

• A. 1 calories/sec
• B. 2 calories/sec
• C. 3 calories/sec
• D. 4 calories/sec

Answer 1

The correct option is B 2 calories/sec

Heat generated per sec $P=\frac{V^2}{R}$

For $5\Omega$ : $10=\frac{V^2}{5}$ $⟹V=5\sqrt{2}$ volts

Thus voltage across $4\Omega$, $V^{\prime }=\frac{4}{4+6}V=\frac{4}{10}\times 5\sqrt{2}=2\sqrt{2}$ volts

$\therefore$ Heat generated per sec in $4\Omega$, $P^{\prime }=\frac{(V^{\prime }{)}^2}{4}=\frac{8}{4}=2$ calories/sec