The circuit shown in Figure P 8.3-8 is at steady state before the switch opens at time t

The circuit shown in Figure P 8.3-1 is at steady state before the switch closes at time t = 0. The input to the circuit is the voltage of the voltage source, 12 V. The output of this circuit is the voltage across the capacitor, v(t). Determine v(t) for t > 0.

The circuit shown in Figure P 8.3-2 is at steady state before the switch opens at time t = 0. The input to the circuit is the voltage of the voltage source, 12 V. The output of this circuit is the current in the inductor, i(t). Determine i(t) for t > 0.

The circuit shown in Figure P 8.3-3 is at steady state before the switch closes at time t = 0. Determine the capacitor voltage v(t) for t > 0.

The circuit shown in Figure P 8.3-4 is at steady state before the switch closes at time t = 0. Determine the inductor current i(t) for t > 0.

The circuit shown in Figure P 8.3-5 is at steady state before the switch opens at time t = 0. Determine the voltage \(v_o\)(t) for t > 0.

The circuit shown in Figure P 8.3-6 is at steady state before the switch opens at time t = 0. Determine the voltage \(v_o\)(t) for t > 0.

Figure P 8.3-7a shows astronaut Dale Gardner using the manned maneuvering unit to dock with the spinning Westar VI satellite on November 14, 1984. Gardner used a large tool called the apogee capture device (ACD) to stabilize the satellite and capture it for recovery, as shown in Figure P 8.3-7a. The ACD can be modeled by the circuit of Figure P 8.3-7b. Find the inductor current \(i_L\) for t > 0.

The circuit shown in Figure P 8.3-8 is at steady state before the switch opens at time t = 0. The input to the circuit is the voltage of the voltage source, \(V_s\). This voltage source is a dc voltage source; that is, \(V_s\) is a constant. The output of this circuit is the voltage across the capacitor, \(v_o\)(t). The output voltage is given by \(v_o(t) = 2 + 8e^{-0.5t}\) V for t > 0 Determine the values of the input voltage \(V_s\), the capacitance C, and the resistance R.

The circuit shown in Figure P 8.3-9 is at steady state before the switch closes at time t = 0. The input to the circuit is the voltage of the voltage source, 24 V. The output of this circuit, the voltage across the 3-\(\Omega\) resistor, is given by \(v_o(t) = 6 - 3e^}-0.35t}\) V when t > 0 Determine the value of the inductance L and of the resistances \(R_1\) and \(R_2\).

A security alarm for an office building door is modeled by the circuit of Figure P 8.3-10. The switch represents the door interlock, and v is the alarm indicator voltage. Find v(t) for t > 0 for the circuit of Figure P 8.3-10. The switch has been closed for a long time at t = 0^-.

The voltage v(t) in the circuit shown in Figure P 8.3-11 is given by \(v(t) = 8 + 4e^{-2t}\) V for t > 0 Determine the values of \(R_1\), \(R_2\), and C.

The circuit shown in Figure P 8.3-12 is at steady state when the switch opens at time t = 0. Determine i(t) for \(t \geq 0\).

The circuit shown in Figure P 8.3-13 is at steady state when the switch opens at time t = 0. Determine v(t) for \(t \geq 0\).

The circuit shown in Figure P 8.3-14 is at steady state when the switch closes at time t = 0. Determine i(t) for \(t \geq 0\).

The circuit in Figure P 8.3-15 is at steady state before the switch closes. Find the inductor current after the switch closes. Hint: i(0) = 0.1 A, \(I_sc\) = 0.3 A, \(R_t\) = 40 \(\Omega\)

Consider the circuit shown in Figure P 8.3-16. (a) Determine the time constant \(\tau\) and the steady-state capacitor voltage when the switch is open. (b) Determine the time constant \(\tau\) and the steady-state capacitor voltage when the switch is closed.

The circuit shown in Figure P 8.3-17 is at steady state before the switch closes. The response of the circuit is the voltage v(t). Find v(t) for t > 0. Hint: After the switch closes, the inductor current is \(i(t)=\) \(0.2\left(1-e^{-1.8 t}\right) \mathrm{A}\)

The circuit shown in Figure P 8.3-18 is at steady state before the switch closes. The response of the circuit is the voltage v(t). Find v(t) for t > 0.

The circuit shown in Figure P 8.3-19 is at steady state before the switch closes. Find v(t) for \(t \geq 0\).

The circuit shown in Figure P 8.3-20 is at steady state before the switch closes. Determine i(t) for \(t \geq 0\).

The circuit in Figure P 8.3-21 is at steady state before the switch closes. Determine an equation that represents the capacitor voltage after the switch closes.

The circuit shown in Figure P 8.3-22 is at steady state when the switch closes at time t ¼ 0. Determine i(t) for \(t \geq 0\).

The circuit in Figure P 8.3-23 is at steady state before the switch closes. Determine an equation that represents the inductor current after the switch closes.

Consider the circuit shown in Figure P 8.3-24a and corresponding plot of the inductor current shown in Figure P 8.3-24b. Determine the values of L, \(R_1\), and \(R_2\). Hint: Use the plot to determine values of D, E, F, and a such that the inductor current can be represented as \(i(t)=\left\{\begin{array}{l} D \text { for } t \leq 0 \\ E+F e^{-a t} \text { for } t \geq 0 \end{array}\right.\)

Consider the circuit shown in Figure P 8.3-25a and corresponding plot of the voltage across the \(40-\Omega\) resistor shown in Figure P 8.3-25b. Determine the values of L and \(R_2\). Hint: Use the plot to determine values of D, E, F, and a such that the voltage can be represented as \(v(t)=\left\{\begin{array}{l} D \text { for } t<0 \\ E+F e^{-a t} \text { for } t>0 \end{array}\right.\)

Determine \(v_o\)(t) for t > 0 for the circuit shown in Figure P 8.3-26.

The circuit shown in Figure P 8.3-27 is at steady state before the switch closes at time t = 0. After the switch closes, the inductor current is given by \(i(t)=0.6-0.2 e^{-5 t} \text { A for } t \geq 0\) Determine the values of \(R_1, R_2\), and L.

After time t = 0, a given circuit is represented by the circuit diagram shown in Figure P 8.3-28. (a) Suppose that the inductor current is \(i(t)=21.6+28.4 e^{-4 t} \mathrm{~mA} \text { for } t \geq 0\) Determine the values of \(R_1\) and \(R_3\). (b) Suppose instead that \(R_1=16 \Omega, R_3=20 \Omega\), and the initial condition is i(0) = 10 mA. Determine the inductor current for \(t \geq 0\).

Consider the circuit shown in Figure P 8.3-29. (a) Determine the time constant \(\tau\) and the steady-state capacitor voltage \(v(\infty)\) when the switch is open. (b) Determine the time constant \(\tau\) and the steady-state capacitor voltage \(v(\infty)\) when the switch is closed.