Write the differential equation for $t>0$ for $v_C$ in Eigure P4.41. Assume $S_1$ is open, $S_2$ is closed and that $R_1=5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2 =4 \mathrm{~F}$.

Narayan Hari

Numerade Educator

07:29

Problem 8

Write the differential equation for $t>0$ for $i_C$ in Eigure P4.47. Assume $V_S=9 \mathrm{~V}$, $C=1 \mu \mathrm{~F}, R_S=5 \mathrm{k} \Omega, R_1=10 \mathrm{k} \Omega$, and $R_2=R_3=20 \mathrm{k} \Omega$.

Narayan Hari

Numerade Educator

Problem 9

Write the differential equation for $t>0$ for $i_L$ in Eigure P4.49.

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Problem 10

Write the differential equations for $t>0$ for $i_L$ and $v_1$ in Eigure P4.52 How are they related? Assume $L_1=1 \mathrm{H}$ and $L_2=5 \mathrm{H}$.

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Problem 12

Determine the initial and final conditions on $v_C$ in Figure P4.23.

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Problem 13

Determine the initial and final conditions on $i_C$ in Figure P4.27.

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03:14

Problem 14

Determine the initial and final conditions on $i_L$ in Figure P4.29.

Thomas Thompson

Numerade Educator

03:09

Problem 15

Determine the initial and final conditions on $v_C$ in Figure P4.32.

Khoobchandra Agrawal

Numerade Educator

Problem 16

Determine the initial and final conditions on $i_C$ and $v_3$ in Eigure P4.34.

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Problem 17

Determine the initial and final conditions on $v_C$ in Eigure P4.41. Assume $S_1$ is always open and $S_2$ is closed at $t=0$.

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Problem 18

Determine the initial and final conditions on $i_C$ in Eigure P4.47. Assume $V_S=9 \mathrm{V}, C=1 \mu \mathrm{~F}, R_S=5 \mathrm{k} \Omega, R_1=10 \mathrm{k} \Omega$, and $R_2=R_3=20 \mathrm{k} \Omega$.

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03:14

Problem 19

Determine the initial and final conditions on $i_L$ in Eigure P4.49.

Thomas Thompson

Numerade Educator

Problem 20

Determine the initial and final conditions on $i_L$ and $v_1$ in Eigure P4.52. Assume $L_1=1 \mathrm{H}$ and $L_2=5 \mathrm{H}$.

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Problem 21

At $t=0^{-}$, just before the switch is opened, the current through the inductor in Figure P4.21 is $i_L=140 \mathrm{~mA}$. Is this value the same as that for DC steady-state? Was the circuit in steady state just before the switch was opened? Assume $V S= 10 \mathrm{~V}, R_1=1 \mathrm{k} \Omega, R_2=5 \mathrm{k} \Omega, R_3=2 \mathrm{k} \Omega$, and $L=1 \mathrm{mH}$.
(FIGURE CAN'T COPY)
Figure P4.21

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05:16

Problem 22

For $t<0$, the circuit shown in Figure P4.22 is at DC steady-state. The switch is thrown at $t=0$.
$$V S 1=35 \mathrm{~V} V S 2=130 \mathrm{~V}$$
$$
\begin{array}{ll}
V_{s 1}=35 \mathrm{~V} & V_{\text {xi }}=130 \mathrm{~V} \\
C=11 \mu \mathrm{~F} & R_1=17 \mathrm{k} \Omega \\
R_2=7 \mathrm{k} \Omega & R_3=23 \mathrm{k} \Omega
\end{array}
$$
Determine the current through $R_3$ just after the switch is thrown at $t=0^{+}$.
(FIGURE CAN'T COPY)
Figure P4.22

Amit Srivastava

Numerade Educator

Problem 23

Determine the current $i_C$ through the capacitor just before and just after the switch is closed in Eigure P4.23. Assume steady-state conditions for $t<0 . V_1= 15 \mathrm{~V}, R_1=0.5 \mathrm{k} \Omega, R_2=2 \mathrm{k} \Omega$, and $C=0.4 \mu \mathrm{~F}$.
(FIGURE CAN'T COPY)
Figure P4.23

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Problem 24

Assume the switch in Eigure P4.23 has been closed for a very long time and then is opened. Determine the current $i_C$ through the capacitor immediately after the switch is opened. $V_1=10 \mathrm{~V}, R_1=200 \mathrm{~m} \Omega, R_2=5 \mathrm{k} \Omega$, and $C=300 \mu \mathrm{~F}$.

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Problem 25

Just before the switch is opened at $t=0$ in Eigure P4.21, assume the current through the inductor Page 318is $i_L=1.5 \mathrm{~mA}$. Determine the voltage $v_3$ across $R_3$ immediately after the switch is opened. Assume $V_S=12 \mathrm{~V}, R_1=6 \mathrm{k} \Omega, R_2=6 \mathrm{k} \Omega, R_3=3 \mathrm{k} \Omega$, and $L=0.9 \mathrm{mH}$.

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Problem 26

Assume that steady-state conditions exist in the circuit shown in Eigure P4.26 for $t<0$. Determine the current through the inductor immediately after the switch is thrown. Assume $L=0.5 \mathrm{H}, R_1=100 \mathrm{k} \Omega, R_S=5 \Omega$, and $V_S=24 \mathrm{~V}$.
(FIGURE CAN'T COPY)
Figure P4.26

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Problem 27

Assume that steady-state conditions exist in the circuit shown in Figure P4.27 for $t<0$ and that $V_1=15 \mathrm{~V}, R_1=100 \Omega, R_2=1.2 \mathrm{k} \Omega, R_3=400 \Omega, C=4.0 \mu \mathrm{~F}$. Determine the current $i_C$ through the capacitor at $t=0^{+}$, just after the switch is closed.
(FIGURE CAN'T COPY)
Figure P4.27

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Problem 28

For $t>0$, find the Norton equivalent network seen by the inductor in Figure P4.28. Use that result to determine the associated time constant. Assume:
$$
\begin{array}{ll}
V_1=12 \mathrm{~V} & V_2=5 \mathrm{~V} \\
L=3 \mathrm{H} & R_3=R_2=2 \Omega \\
R_3=4 \Omega &
\end{array}
$$
(FIGURE CAN'T COPY)
Figure P4.28

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Problem 29

For $t>0$, find the Norton equivalent network seen by the inductor in Figure P4.29. Use that result to determine the associated time constant. Assume:
(FIGURE CAN'T COPY)
Figure P4.29

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01:14

Problem 30

For $t>0$, find the Thévenin equivalent network seen by the capacitor in Eigure P4.30 Use that result to determine the associated time constant. Assume: $R_1=3 \Omega, R_2=1 \Omega, R_3=4 \Omega, C=0.2 \mathrm{~F}, I_S=3 \mathrm{~A}$.
(FIGURE CAN'T COPY)
Figure P4.30

Varsha Aggarwal

Numerade Educator

05:46

Problem 31

For $t>0$, find the Thévenin equivalent network seen by the capacitor in Eigure P4.31. Use that result to determine the associated time constant. Assume: $R_S=8 \mathrm{k} \Omega, V_S=40 \mathrm{~V}, C=350 \mu \mathrm{~F}$, and $R=24 \mathrm{k} \Omega$.
(FIGURE CAN'T COPY)
Figure P4.31

Mederic Rodriguez

Numerade Educator

Problem 32

Determine the voltage $v_C$ across the capacitor shown in Figure P4.32 for $t>0$.
Assume a DC steady-state for $t<0$ and:
$$
\begin{array}{ll}
I_a=17 \mathrm{~mA} & C=0.55 \mu \mathrm{~F} \\
R_1=7 \mathrm{k} \Omega & R_2=3.3 \mathrm{k} \Omega
\end{array}
$$
(FIGURE CAN'T COPY)
Figure P4.32

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Problem 33

For $t<0$, the circuit shown in Figure P4.29 is at steady state. The switch is thrown at $t=0$. Determine the current $i_L$ through the inductor for $t>0$. Assume:

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Problem 34

For $t<0$, the circuit shown in Eigure P4.34 is at steady state. The switch is thrown at $t=0$. Assume:
$$
\begin{array}{ll}
V_n=17 \mathrm{~V} & V_{32}=11 \mathrm{~V} \\
R_1=14 \mathrm{k} \Omega & R_2=13 \mathrm{k} \Omega \\
R_3=14 \mathrm{k} \Omega & C=70 \mathrm{nF}
\end{array}
$$
Determine the
a. Current $i_C$ through the capacitor for $t>0$.
b. Voltage $v_3$ across $R_3$ for $t>0$.
c. Time required for $i_C$ and $v_3$ to change by 98 percent of their initial values at $t=0^{+}$.
(FIGURE CAN'T COPY)
Figure P4.34

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00:39

Problem 35

The circuit in Figure P4,35 is a simple model of an automotive ignition system. The switch models the "points" that switch electric power to the cylinder when the fuel-air mixture is compressed. $R$ is the resistance across the gap between the electrodes of the spark plug.
$$
\begin{array}{ll}
V_G=12 \mathrm{~V} & R_G=0.37 \Omega \\
R=1.7 \mathrm{k} \Omega &
\end{array}
$$
Determine the value of $L$ and $R_1$ so that the voltage across the spark plug gap just after the switch is changed is 23 kV and so that this voltage will change exponentially with a time constant $\tau=13 \mathrm{~ms}$.
(FIGURE CAN'T COPY)
Figure P4.35

Varsha Aggarwal

Numerade Educator

Problem 36

The inductor $L$ in the circuit shown in Figure P4.36 is the coil of a relay. When the current $i_L$ through the coil is equal to or greater than 2 mA , the relay is activated. Assume DC steady-state conditions at $t<0$ and the following values:
$$
\begin{aligned}
& V_5=12 \mathrm{~V} \\
& L=10.9 \mathrm{mH} \\
& R_1=3.1 \mathrm{k} \mathrm{\Omega}
\end{aligned}
$$
Determine $R_2$ so that the relay activates 2.3 seconds after the switch is thrown.
(FIGURE CAN'T COPY)
Figure P4.36

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Problem 37

Determine the current $i_C$ through the capacitor in Eigure P4.37 for all time. Assume DC steady-state conditions for $t<0$. Also assume: $V_1=10 \mathrm{~V}, C=200 \mu \mathrm{F}, R_1=300 \mathrm{~m} \Omega$, and $R_2=R_3=1.2 \mathrm{k} \Omega$.
(FIGURE CAN'T COPY)
Figure P4.37

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Problem 38

Determine the voltage $v_L$ across the inductor in Figure P4.38 for all time. Assume DC steady-state conditions for $t<0$. Also assume: $V_S=15 \mathrm{~V}, L=200 \mathrm{mH}, R_S=1 \Omega$, and $R_1=20 \mathrm{k} \Omega$.
(FIGURE CAN'T COPY)
Figure P4.38

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Problem 39

For $t<0$, the circuit shown in Eigure P4.39 is at DC steady-state. The switch is closed at $t=0$. Determine the voltage $v_C$ for all time. Assume: $R_1=R_3=3 \Omega, R_2 =6 \Omega, V_1=15 \mathrm{~V}$, and $C=0.5 \mathrm{~F}$.
(FIGURE CAN'T COPY)
Figure P4.39

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Problem 40

For $t<0$, the circuit shown in Figure P4.21 is at DC steady-state. The switch is opened at $t=0$. Determine the current $i_L$ through the inductor for all time. Assume:
$$
\begin{array}{ll}
V_s=12 \mathrm{~V} & L=100 \mathrm{mH} \\
R_1=400 \Omega & R_2=400 \Omega \\
R_3=600 \Omega &
\end{array}
$$

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Problem 41

For the circuit shown in Figure P4.41, assume that switch $S_1$ is always held open and that switch $S_2$ is open until being closed at $t=0$. Assume DC steady-state conditions for $t<0$. Also assume $R_1=5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0^{+}$.
b. Find the time constant $\tau$ for $t>0$.
c. Find $v_C$ for all time and sketch the function.
d. Evaluate the ratio $v_C$ to $v_C(\infty)$ at each of the following times: $t=0, \tau, 2 \tau$, $5 \tau, 10 \tau$.
(FIGURE CAN'T COPY)
Figure P4.41

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Problem 42

For the circuit shown in Figure P4,41, assume that switches $S_1$ and $S_2$ have been held open and closed, respectively, for a long time prior to $t=0$. Then, simultaneously at $t=0, S_1$ closes and $S_2$ opens. Also assume $R_1=5 \Omega, R_2=4 \Omega$, $R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0^{+}$.
b. Find the time constant $\tau$ for $t>0$.
c. Find $v_C$ for all time and sketch the function.
d. Evaluate the ratio $v_C$ to $v_C(\infty)$ at each of the following times: $t=0, \tau, 2 \tau$, $5 \tau, 10 \tau$.

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Problem 43

For the circuit shown in Eigure P4.41, assume that switch $S_2$ is always held open and that switch $S_1$ is closed until being opened at $t=0$. Subsequently, $S_1$ closes at $t=3 \tau$ and remains closed. Also assume DC steady-state conditions for $t<0$ and $R_1=5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega, C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0$.
b. Find $v_C$ for $0<t<3 \tau$.
c. Use part b to find the capacitor voltage $v_C$ at $t=3 \tau$, and use it to find $v_C$ for $t>3 \tau$.
d. Compare the two time constants for $0<t<3 \tau$ and $t>3 \tau$.
e. Sketch $v_C$ for all time.

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Problem 44

For the circuit shown in Eigure P4.41, assume that switches $S_1$ and $S_2$ have been held open for a long time prior to $t=0$ but then close at $t=0$. Also assume $R_1= 5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0$.
b. Find the time constant $\tau$ for $t>0$.
c. Find $v_C$ and sketch the function.
d. Evaluate the ratio $v_C$ to $v_C(\infty)$ at each of the following times: $t=0, \tau, 2 \tau$, $5 \tau, 10 \tau$.

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Problem 45

For the circuit shown in Figure P4.41, assume that switches $S_1$ and $S_2$ have been held closed for a long time prior to $t=0 . S_1$ then opens at $t=0$; however, $S_2$ does not open until $t=48 \mathrm{~s}$. Also assume $R_1=5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0$.
b. Find the time constant $\tau$ for $0<t<48 \mathrm{~s}$.
c. Find $v_C$ for $0<t<48 \mathrm{~s}$.
d. Find $\tau$ for $t>48 \mathrm{~s}$.
e. Find $v_C$ for $t>48 \mathrm{~s}$.
f. Sketch $v_C$ for all time.

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Problem 46

For the circuit shown in Figure P4.41, assume that switches $S_1$ and $S_2$ have been held closed for a long time prior to $t=0 . S_2$ then opens at $t=0$; however, $S_1$ does not open until $t=96 \mathrm{~s}$. Also assume $R_1=5 \Omega, R_2=4 \Omega, R_3=3 \Omega, R_4=6 \Omega$, and $C_1=C_2=4 \mathrm{~F}$.
a. Find the capacitor voltage $v_C$ at $t=0$.
b. Find the time constant for $0<t<96 \mathrm{~s}$.
c. Find $v_C$ for $0<t<96 \mathrm{~s}$.
d. Find the time constant for $t>96 \mathrm{~s}$.
e. Use part c to find the capacitor voltage $v_C$ at $t=96 \mathrm{~s}$, and use it to find $v_C$ for $t>96 \mathrm{~s}$
f. Sketch $v_C$ for all time.

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01:14

Problem 47

For the circuit in Figure P4.47, determine the value of resistors $R_1$ and $R_2$, knowing that the time constant before the switch opens is 1.5 ms , and it is 10 ms after the switch opens. Assume: $R_S=15 \mathrm{k} \Omega, R_3=30 \mathrm{k} \Omega$, and $C=1 \mu \mathrm{~F}$.
(FIGURE CAN'T COPY)
Figure P4.47

Varsha Aggarwal

Numerade Educator

03:40

Problem 48

For the circuit in Figure P4.47, assume $V_S=100 \mathrm{~V}, R_S=4 \mathrm{k} \Omega, R_1=2 \mathrm{k} \Omega, R_2= R_3=6 \mathrm{k} \Omega, C=1 \mu \mathrm{~F}$, and the circuit is in a steady-state condition before the switch opens. Find the value of $v_C$ at $t=8 / 3 \mathrm{~ms}$ after the switch opens.

Narayan Hari

Numerade Educator

Problem 49

In the circuit in Figure P4.49, how long after the switch is thrown at $t=0$ will $i_L =5 \mathrm{~A}$ ? Assume a DC steady-state for $t<0$. Plot $i_L(t)$.
(FIGURE CAN'T COPY)
Figure P4.49

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01:23

Problem 50

Refer to Eigure P4.49 and assume that the switch takes 5 ms to move from one contact to the other. Also assume that during this time neither switch position has electrical contact. Find:
a. $i_L(t)$ for $0<t<5 \mathrm{~ms}$.
b. The maximum voltage between the contacts during the $5-\mathrm{ms}$ duration of the switching.

Andreas Papavassiliou

Numerade Educator

11:13

Problem 51

The circuit in Figure P4.51 includes a voltage-controlled switch. The switch closes or opens when the voltage across the capacitor reaches the value $v_m^{\mathrm{c}}$ or $v_m^{\mathrm{c}}$, respectively. If $v_M^{\circ}=1$ and the period of the capacitor voltage waveform is 200 ms , find $v_{\mathrm{M}}^{\mathrm{c}}$.
(FIGURE CAN'T COPY)
Figure P4.51

Artemisa Mazón

Numerade Educator

Problem 52

At $t=0$ the switch in the circuit in Figure P4.52 closes. Assume that $L_1=1 \mathrm{H}$, $L_2=5 \mathrm{H}$, and that the circuit is in DC steady-state for $t<0$. Find $i_L(t)$ for all time.
(FIGURE CAN'T COPY)
Figure P4.52

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Problem 53

Repeat Problem P4.52 to find $v_1(t)$ for all time.

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02:43

Problem 54

The analogy between electrical and thermal systems can be used to analyze the behavior of a pot heating on an electric stove. The heating element is modeled as shown in Figure P4.54. Find the "heat capacity" of the burner, $C_S$, if the burner reaches 90 percent of the desired temperature in 10 s . Assume $R_S=1.5 \Omega$.
(FIGURE CAN'T COPY)
Figure P4.54

Ren Jie Tuieng

Numerade Educator

06:56

Problem 55

The burner and pot of Problem 4.54 can be modeled as shown in Eigure P4.55. $R_0$ models the thermal loss between the burner and the pot. The pot is modeled by a thermal capacitance $C_P$ in parallel with a thermal resistance $R_P$.
a. Find the final temperature of the water in the pot-that is, find $v_o$ as $t \rightarrow \infty$ if $I_S=75 \mathrm{~A}, C_P=80 \mathrm{~F}, R_0=0.8 \Omega, R_P=2.5 \Omega$, and the bumer is the same as in Problem 4.54.
b. How long will it take for the water to reach 80 percent of its final temperature?
(FIGURE CAN'T COPY)
Figure P4.55

Khoobchandra Agrawal

Numerade Educator

01:18

Problem 56

The circuit in Eigure P4.56 is used as a variable delay in a burglar alarm. The alarm is a siren with an internal resistance of $1 \mathrm{k} \Omega$. The alarm will not sound until the current $i_0$ exceeds $100 \mu \mathrm{~A}$. Use a graphical solution or a computer simulation to find the range of the variable resistor $R$ for which the delay is between 1 and 2 s . Assume the capacitor is initially uncharged.
(FIGURE CAN'T COPY)
Figure P4.56

Charles Magnusen

Numerade Educator

Problem 57

For $t>0$, find the voltage $v_1$ across $C_1$ shown in Eigure P4.57. Let $C_1=5 \mu \mathrm{~F}$ and $C_2=10 \mu \mathrm{~F}$. Assume the capacitors are initially uncharged.
(FIGURE CAN'T COPY)
Figure P4.57

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03:31

Problem 58

For the circuit shown in Eigure P4.58 determine the time constants when the switch is open and when it is closed.
Figure P4.58

Sikandar Baig

Numerade Educator

07:53

Problem 59

The circuit in Figure P4.59 models the charging circuit of an electronic camera flash. The flash should be charged to $v_C \leq 7.425 \mathrm{~V}$ for each use. Assume $C=1.5 \mathrm{mF}, R_1=1 \mathrm{k} \Omega$, and $R_2=1 \Omega$.
a. How long does it take the flash to recharge after taking a picture?
b. The shutter button stays closed for $1 / 30 \mathrm{~s}$. How much energy is delivered to the flash bulb $R_2$ in that interval? Assume the capacitor is fully charged.
c. If the shutter button is pressed 3 s after a flash, how much energy is delivered to the bulb $R_2$ ?
(FIGURE CAN'T COPY)
Figure P4.59

Ren Jie Tuieng

Numerade Educator

Problem 60

The ideal current source $i_s(t)$ in Figure P4.60 switches levels as shown. Determine and sketch the voltage $v_o(t)$ across the inductor for $0<t<2 \mathrm{~s}$. Assume the inductor current is zero before $t=0, R_S=500 \Omega$, and $L=50 \mathrm{H}$.
(FIGURE CAN'T COPY)
Figure P4.60

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Problem 61

In the circuit shown in Figure P4.61:
Determine the voltage $v_C$ across the capacitor and the current $i_L$ through the inductor as $t \rightarrow \infty$.
(FIGURE CAN'T COPY)
Figure P4.61

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Problem 62

For $t>0$, determine the current $i_L$ through the inductor and the voltage $v_C$ across the capacitor in Figure P4.62. Assume $v_S=-1 \mathrm{~V}$ for $t<0$ but is reversed to $v_S=$ 1 V for $t>0$. Also assume $R=10 \Omega, L=5 \mathrm{mH}, C=100 \mu \mathrm{~F}$, and that the circuit was in DC steady-state prior to when the source was reversed.
(FIGURE CAN'T COPY)
Figure P4.62

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Problem 63

The switch shown in Eigure P4.63 closes at $t=0$. Assume a DC steady-state for $t<0$ and:
Determine the current $i_L$ through the inductor and the voltage $v_C$ across the capacitor for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.63

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Problem 64

The switch in the circuit shown in Eigure P4.64 closes at $t=0$. Assume a DC steady-state for $t<0$ and:
$$
\begin{array}{ll}
V_5=12 \mathrm{~V} & C=130 \mu \mathrm{~F} \\
R_1=2.3 \mathrm{k} \Omega & R_2=7 \mathrm{k} \Omega \\
L=30 \mathrm{mH} &
\end{array}
$$
Determine the current $i_L$ through the inductor and the voltage $v_C$ across the capacitor for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.64

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Problem 65

The switch shown in Figure P4.65 is thrown at $t=0$. Assume a DC steady-state for $t<0$ and:
$$
\begin{array}{ll}
V_5=12 \mathrm{~V} & R_5=100 \Omega \\
R_1=31 \mathrm{k} \Omega & R_2=22 \mathrm{k} \Omega \\
L=0.9 \mathrm{mH} & C=0.5 \mu \mathrm{~F}
\end{array}
$$
Determine the current $i_1$ through $R_1$ and the voltage $v_2$ across $R_2$ for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.65

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Problem 66

For $t<0$, the circuit shown in Eigure P4.66 is at DC steady-state and the voltage across the capacitor is +7 V . The switch is thrown at $t=0$. Assume:
$$
\begin{array}{ll}
V_s=12 \mathrm{~V} & C=3,300 \mu \mathrm{~F} \\
R_1=9.1 \mathrm{k} \Omega & R_2=4.3 \mathrm{k} \Omega \\
R_3=4.3 \mathrm{k} \Omega & L=16 \mathrm{mH}
\end{array}
$$
Determine the current $i_L$ through the inductor, the voltage $v_C$ across the capacitor, and the current $i_2$ through $R_2$ for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.66

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Problem 67

For $t<0$, the circuit shown in Figure P4.67 is in DC steady-state. Determine the current $i_L$ through the inductor and the voltage $v_C$ across the capacitor for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.67

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Problem 68

For $t<0$, the circuit shown in Eigure P4.68 is in DC steady-state. The switch is closed at $t=0$. Determine the current $i_L$ through the inductor and the voltage $v_C$ across the capacitor for $t>0$. Assume $R=3 \mathrm{k} \Omega, R_S=600 \Omega, V_S=2 \mathrm{~V}, C=2$ mF , and $L=1 \mathrm{mH}$.
(FIGURE CAN'T COPY)
Figure P4.68

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Problem 69

Assume the switch in the circuit in Eigure P4. 69 has been closed for a very long time. It is suddenly opened at $t=0$ and then reclosed at $t=5 \mathrm{~s}$. Determine the current $i_L$ through the inductor, the voltage $v_C$ across the capacitor, and the voltage $v$ across the $2-\Omega$ resistor for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.69

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Problem 70

Determine whether the circuit in Figure P4.70 is overdamped or underdamped for $t>0$. Assume $V_S=15 \mathrm{~V}, R=200 \Omega, L=20 \mathrm{mH}$, and $C=0.1 \mu \mathrm{~F}$. Determine the capacitance that results in critical damping.
(FIGURE CAN'T COPY)
Figure P4.70

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Problem 71

For $t<0$ ，assume the circuit in Figure P4．70 is in DC steady－state．Assume $V_S= 15 \mathrm{~V}, R=200 \Omega, L=20 \mathrm{mH}$ and $C=0.1 \mu \mathrm{~F}$ ．If the switch is thrown at $t=0$ ，find the：
a．Initial capacitor voltage $v_C$ at $t=0^{+}$．
b．Capacitor voltage $v_C$ at $t=20 \mu \mathrm{~s}$ ．
c．Capacitor voltage $v_C$ as $t \rightarrow \infty$ ．
d．Maximum capacitor voltage．

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02:19

Problem 72

Assume the switch in the circuit in Figure P4．69 has been open for a very long time．It is suddenly closed at $t=0$ and then reopened at $t=5 \mathrm{~s}$ ．Determine the current $i_L$ through the inductor，the voltage $v_C$ across the capacitor，and the voltage $v$ across the $2-\Omega$ resistor for $t>0$ ．

Keshav Singh

Numerade Educator

Problem 73

Assume that the circuit shown in Figure P4．70 is underdamped，and for $t<0$ ， the circuit is in DC steady－state with $v_C=V_S$ ．After the switch is thrown at $t=0$ ， the first two zero crossings of the capacitor voltage $\nu_C$ occur at $t=5 \pi / 3 \mu \mathrm{~s}$ and $t =5 \pi \mu \mathrm{~s}$ ．At $t=20 \pi / 3 \mu \mathrm{~s}$ ，the capacitor voltage $v_C$ peaks at $0.6 V_S$ ．If $C=1.6 \mu \mathrm{~F}$ ， what are the values of $R$ and $L$ ？

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Problem 74

Given the information provided in Problem 4．73，what are the values of $R$ and $L$ so that the peak at $20 \pi / 3 \mu \mathrm{~s}$ is $v_C=0.7 V_S$ ？Assume $C=1.6 \mu \mathrm{~F}$ ．

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Problem 75

Determine $i_L$ for $t>0$ in Figure P4．75，assuming $i_L(0)=2.5 \mathrm{~A}$ and $v_C(0)=10 \mathrm{~V}$ ．
(FIGURE CAN'T COPY)
Figure P4.75

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Problem 76

Find the maximum value of $v_C$ for $t>0$ in Figure P4．76，assuming DC steady－ state for $t<0$ ．
(FIGURE CAN'T COPY)
Figure P4.76

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Problem 77

For $t>0$, determine the time $t$ at which $i=2.5 \mathrm{~A}$ in Figure P4.77, assuming DC steady-state for $t<0$.
(FIGURE CAN'T COPY)
Figure P4.77

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Problem 78

For $t>0$, determine the time $t$ at which $i=6 \mathrm{~A}$ in Eigure P4.78, assuming DC steady-state for $t<0$.
(FIGURE CAN'T COPY)
Figure P4.78

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Problem 79

For $t>0$, determine the time $t$ at which $v=7.5 \mathrm{~V}$ in Figure P4.79, assuming DC steady-state for $t<0$.
(FIGURE CAN'T COPY)
Figure P4.79

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Problem 80

Assume the circuit in Eigure P4.80 is in DC steady-state for $t<0$ and $L=3 \mathrm{H}$. Find the maximum value of $v_C$ for $t>0$.
(FIGURE CAN'T COPY)
Figure P4.80

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03:40

Problem 81

Assume the circuit in Figure P4.80 is in DC steady-state for $t<0$. Find the value of the inductance $L$ that makes the circuit critically damped for $t>0$. Find the maximum value of $v_C$ for $t>0$.

Narayan Hari

Numerade Educator

Problem 82

For $t>0$, determine $v$ in Figure P4.82, assuming DC steady-state for $t<0$.
(FIGURE CAN'T COPY)
Figure P4.82

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