Capacitor Switching and Joule Heat

Problem Statement

A circuit consists of a DC source with EMF $V$V, capacitor $C_1$C1​ with capacitance $C_1$C1​, capacitor $C_2$C2​ with capacitance $C_2$C2​, resistor $R_1$R1​ with resistance $R_1$R1​, resistor $R_2$R2​ with resistance $R_2$R2​, and switches $S_1, S_2$S1​,S2​.

There is a closed loop running from the positive terminal of the source through switch $S_1$S1​, resistor $R_1$R1​, capacitor $C_1$C1​, and back to the negative terminal of the source. In addition, in parallel with capacitor $C_1$C1​, there is a series connection of switch $S_2$S2​, resistor $R_2$R2​, and capacitor $C_2$C2​ (i.e., connected from the positive plate of $C_1$C1​ through $S_2$S2​, $R_2$R2​, $C_2$C2​ to the negative plate of $C_1$C1​).

Initially, both switches $S_1$S1​ and $S_2$S2​ are open, and no charge is stored in capacitors $C_1$C1​ or $C_2$C2​.

The following operations are performed in sequence: [Operation 1] Switch $S_1$S1​ is closed and sufficient time passes. [Operation 2] Switch $S_1$S1​ is then opened, followed by closing switch $S_2$S2​ and waiting until sufficient time passes.

Find the Joule heat $J$J generated in the circuit during Operation 2.

Constraints

• $V = 120 \ \text{V}$V=120 V
• $C_1 = 4.0 \times 10^{-6} \ \text{F}$C1​=4.0×10−6 F
• $C_2 = 6.0 \times 10^{-6} \ \text{F}$C2​=6.0×10−6 F
• $R_1 = 100 \ \Omega$R1​=100 Ω
• $R_2 = 200 \ \Omega$R2​=200 Ω

Input Format

Find the Joule heat $J$J in $\mu\text{J}$μJ (microjoules) and give the answer as a positive integer.