Find (a) i, (b) i₁, and (c) i2 in the circuit in Fig. P2.35. Figure P2.35 12 0 www + 18v( ) 60 ਤ 54 $10 º →5 0 +

The circuit shown in Figure P has three inputs: V₁, 12, and v3. The output of the circuit is the current io. The output of the circuit is related to the inputs by To = av1 +biztcV3 where a, b, and c are constants. Determine the values of a, b, and c. 01 T + 20 Ω M ig V3 1 + io www 40 Ω 12 Ω 10 Ω

V1 + I S1 M R1 C1 S2 Figure 4: A circuit with multiple switches L1 R2 Given the circuit in figure 4 with component values R₁ = 10 k2, R₂ = 20 k2, C₁ = 1µF, L₁ = 2 mH, and V₁ = 5 V. All switches are closed, and the circuit has reached steady state (t <0 seconds). At time t = 0 seconds switch S₂ is opened and at time t = 5 seconds switch S₁ is opened. Hint: Take your time to consider carefully what the state is of the circuit for each switch. a) Calculate the voltage over the capacitor for all time b) Calculate the current over the inductor for all time.

a) The circuit below has three resistors with values R₁-10 S2, R₂-20 S2, R3-30 S2, one initially (t=0) uncharged 0.001 F capacitor, and a 30 V battery. Find all the currents at t=0 (right after the switch is closed,) all the currents a long time after the switch is closed (at steady state), and the charge on the capacitor at t→∞. At time ti, once steady state with the switch close has been effectively reached, the switch is reopened. Find the currents at this time, right after reopening the switch. Make sure to make your reasoning clear! R₁ - 18 S www R₂ www. I₁ 12 13 Qc t=0 0 t→∞ T=ti b) What is the maximum rate at which the capacitor's charge changes in the circuit above? c) Explain in words (physics, not math) the steady state current through R3 in the circuit above after a long time with the switch closed, and then a long time after the switch is re-opened (a long time after t₁.) An explanation requires both telling me what it is AND why it is that.