All new homes are required to install a device called a ground fault circuit interrupter

Figure P 14.7-1a shows a circuit represented in the time domain. Figure P 14.7-1b shows the same circuit, now represented in the complex frequency domain. Figure P 14.7-1c shows a plot of the inductor current. Determine the values of D and E, used to represent the circuit in the complex frequency domain. Determine the values of the resistance \(R_2\) and the inductance L.

Figure P 14.7-2a shows a circuit represented in the time domain. Figure P 14.7-2b shows the same circuit, now represented in the complex frequency domain. Figure P 14.7-2c shows a plot of the inductor current. Determine the values of D and E, used to represent the circuit in the complex frequency domain. Determine the values of the resistance \(R_1\) and the capacitance C.

Figure P 14.7-3a shows a circuit represented in the time domain. Figure P 14.7-3b shows the same circuit, now represented in the complex frequency domain. Determine the values of a, b, and d, used to represent the circuit in the complex frequency domain.

The input to the circuit shown in Figure P 14.7-4 is the voltage of the voltage source, 12 V. The output of this circuit is the voltage \(v_o\)(t) across the capacitor. Determine \(v_o\)(t) for t > 0.

The input to the circuit shown in Figure P 14.7-5 is the voltage of the voltage source, 12 V. The output of this circuit is the current i(t) in the inductor. Determine i(t) for t > 0.

The input to the circuit shown in Figure P 14.7-6 is the voltage of the voltage source, 18 V. The output of this circuit, the voltage across the capacitor, is given by \(v_o\)(t) = 6 + \(12e^{-2t}\) V when t > 0 Determine the value of the capacitance C and the value of the resistance R.

The input to the circuit shown in Figure P 14.7-7 is the voltage source voltage \(v_s\)(t) = 3 - u(t) V The output is the voltage \(v_o\)(t) = 10 + \(5e^{-100t}\) V for t \(\geq\) 0 Determine the values of \(R_1\) and \(R_2\).

Determine the inductor current \(i_{\mathrm{L}}(t)\) in the circuit shown in Figure P 14.7-8 for each of the following cases: (a) \(R=2 \Omega, L=4.5 \mathrm{H}, C=1 / 9 \mathrm{~F}, A=5 \mathrm{~mA}, B=-2 \mathrm{~mA}\) (b) \(R=1 \Omega, L=0.4 \mathrm{H}, C=0.1 \mathrm{~F}, A=1 \mathrm{~mA}, B=-2 \mathrm{~mA}\) (c) \(R=1 \Omega, L=0.08 \mathrm{H}, C=0.1 \mathrm{~F}, A=0.2 \mathrm{~mA}, B=\) \(-2 \mathrm{~mA}\)

Determine the capacitor current \(l_{\mathrm{c}}(t)\) in the circuit shown in Figure P 14.7-9 for each of the following cases: (a) \(R=3 \Omega, L=2 \mathrm{H}, C=1 / 24 \mathrm{~F}, A=12 \mathrm{~V}\) (b) \(R=2 \Omega, L=2 \mathrm{H}, C=1 / 8 \mathrm{~F}, A=12 \mathrm{~V}\) (c) \(R=10 \bar{\Omega}, L=2 \mathrm{H}, C=1 / 40 \mathrm{~F}, A=12 \mathrm{~V}\)

The voltage source voltage in the circuit shown in Figure P 14.7-10 is \(v_s(t)=12-6 u(t) \mathrm{V}\) Determine v(t) for t \(\geq\) 0.

Determine the output voltage \(v_o\)(t) in the circuit shown in Figure P 14.7-11.

Determine the capacitor voltage v(t) in the circuit shown in Figure P 14.7-12.

Determine the voltage \(v_o\)(t) for t \(\geq\) 0 for the circuit of Figure P 14.7-13. Hint: \(v_C\)(0) = 4 V

Determine the current \(i_L\)(t) for t \(\geq\) 0 for the circuit of Figure P 14.7-14. Hint: \(v_C\)(0) = 8 V and \(i_L\)(0) = 1 A

The circuit shown in Figure P 14.7-15 is at steady state before the switch opens at time t = 0. Determine the voltage v(t) for t > 0.

The circuit shown in Figure P 14.7-16 is at steady state before time t = 0. Determine the voltage v(t) for t > 0.

The input to the circuit shown in Figure P 14.7-17 is the voltage source voltage \(v_{\mathrm{i}}(t)=10+5 u(t) \mathrm{V}= \begin{cases}10 \mathrm{~V} & \text { when } t<0 \\ 15 \mathrm{~V} & \text { when } t>0\end{cases}\) Determine the response \(v_{\mathrm{o}}(t)\). Assume that the circuit is at steady state when t < 0. Sketch \(v_{\mathrm{o}}(t)\) as a function of t.

The input to the circuit shown in Figure P 14.7-18 is the current source current \(i(t)=25-15 u(t) \mathrm{mA}=\left\{\begin{array}{cl} 25 \mathrm{~mA} & \text { when } t<0 \\ 10 \mathrm{~mA} & \text { when } t>0 \end{array}\right.\) Determine the response \(i_2(t)\). Assume that the circuit is at steady state when t < 0. Sketch \(i_2(t)\) as a function of t.

All new homes are required to install a device called a ground fault circuit interrupter (GFCI) that will provide protection from shock. By monitoring the current going to and returning from a receptacle, a GFCI senses when normal flow is interrupted and switches off the power in 1 / 40 second. This is particularly important if you are holding an appliance shorted through your body to ground. A circuit model of the GFCI acting to interrupt a short is shown in Figure P 14.7-19. Find the current flowing through the person and the appliance, i(t), for t \(\geq\) 0 when the short is initiated at t = 0. Assume v = 160 \cos 400 t and the capacitor is intially uncharged.

Using the Laplace transform, find \(v_{\mathrm{c}}(t)\) for t > 0 for the circuit shown in Figure P 14.7-20. The initial conditions are zero. Hint: Use a source transformation to obtain a single mesh circuit.

Determine the inductor current i(t) in the circuit shown in Figure P 14.7-21.

Find \(v_2\)(t) for the circuit of Figure P 14.7-22 for t \(\geq\) 0. Hint: Write the node equations at a and b in terms of \(v_1\) and \(v_2\). The initial conditions are \(v_1\)(0) = 10 V and \(v_2\)(0) = 25 V. The source is \(v_s\) = 50 cos 2t u(t) V.

The motor circuit for driving the snorkel shown in Figure P 14.7-23a is shown in Figure P 14.7-23b. Find the motor current \(I_2\)(s) when the initial conditions are \(i1\)\((0^-)\) = 2 A and \(i_2\)\((0^-)\) = 3 A. Determine \(i_2\)(t) and sketch it for 10 s. Does the motor current smoothly drive the snorkel?

Using Laplace transforms, find \(v_o\)(t) for t > 0 for the circuit shown in Figure P 14.7-24.

The circuit shown in Figure P 14.7-25 is at steady state before the switch opens at time t = 0. Determine the inductor voltage v(t) for t > 0.

The circuit shown in Figure P 14.7-26 is at steady state before the switch opens at time t = 0. Determine the voltage v(t) for t > 0.