In the circuit given in the figure, switch S is closed at position 1 for long time. Find the total heat generated in resistor of resistance 2r0, when the switch S is open at position 1 and closed at position 2.
C0E203
Step 1: Switch at position 1: Since circuit is in the steady state, the current through circuit is zero. According to the loop rule,
E0−q0C0=0
q0=C0E0
Step 2: Switch at position 2: In this case, total energy stored in capacitor appears as heat energy in the resistor.
ΔH=I2RT,ΔH∝R
ΔH1ΔH2=R1R2=r02r0=12 or ΔH2=2ΔH1
But ΔH=ΔH1+ΔH2=ΔH22+ΔH2=32ΔH2
Therefore ΔH2=23ΔH=23×12C0E20=13C0E20