Question

In the circuit shown in figure switch S is thrown to position 1 at t = 0. When the current in the resistor is 1 A it is then shifted to position 2. The total heat generated in the circuit after shifting to position 2 is

• A. zero
• B. $625\mu J$
• C. $100\mu J$
• D. none of the above

Answer 1

The correct option is C $100\mu J$

In position-1, when the current 1 A flow through resistor so that time potential across the capacitor $=(10-5\times 1)=5V$
Now it is shifted to position-2 where in steady state it is again charge to 5 V, but with opposite polarity.
in both case energy stored is same i.e, $U_i=U_f=\frac{1}{2}C{V}^2$ where $(V=5V)$
Total energy supplied by the lower battery is converted into heat. But double charge transfer (from the normal) takes place from this battery because the batteries are in opposite polarity.
Thus, $\Delta q=CV-(-CV)=2CV$
Heat produced $=$ Energy supplied by the battery $=\Delta qV=2C{V}^2=2\times 2\times {10}^{-6}\times 5^2=100\mu J$