You are given three ideal capacitors and a small resistor. A...

Prompt

You are given three ideal capacitors and a small resistor. All connections are made through the resistor, and you wait until steady state after each connection. The resistor is the only source of energy dissipation. There are no external power sources. Capacitors: - C1 = 2 F, terminals A and B. Initially V_A - V_B = +12 V. - C2 = 3 F, terminals C and D. Initially V_C - V_D = -5 V. - C3 = 6 F, terminals E and F. Initially V_E - V_F = 0 V. Step 1: Connect A to D and B to C. Wait until equilibrium. Step 2: Disconnect everything. Then connect A, C, and E together to form node P, and connect B, D, and F together to form node N. Wait until equilibrium. Tasks: 1. Find the exact final voltage V_P - V_N after Step 2. 2. Find the final total energy stored in all capacitors. 3. Find the total heat dissipated in the resistor over both steps. 4. Show charge conservation explicitly at each step. 5. Explain briefly why total stored energy decreases even though the capacitors and wires are ideal except for the resistor. Give exact rational values where possible.