The heat generated in 1 minute between points $A$ and $B$ in the given circuit, when a battery of 9

Question

The heat generated in 1 minute between points $A$ and $B$ in the given circuit, when a battery of 9 V with internal resistance of $1 \Omega$ is connected across these points is $\_\_\_\_$ J.

Professor PC Thomas Classes · Answer

The given circuit is a balanced Wheatstone bridge because the ratio of resistance in the upper and lower arms are equal $\left(\frac{1\Omega}{2\Omega} = \frac{2\Omega}{4\Omega}ight)$. Thus, no current flows through the central $1\Omega$ resistor. The equivalent resistance between A and B is $R_{AB} = \frac{(1+2)(2+4)}{(1+2)+(2+4)} = \frac{3 	imes 6}{3+6} = 2 \Omega$. The total current from the battery is $I = \frac{V}{R_{AB} + r} = \frac{9}{2+1} = 3 	ext{ A}$. The heat generated between A and B in $t = 60 	ext{ s}$ is $H = I^2 R_{AB} t = (3)^2 	imes 2 	imes 60 = 1080 	ext{ J}$.