Question

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

   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
Show more…
Principles and Applications of Electrical Engineering
Principles and Applications of Electrical Engineering
Giorgio Rizzoni,… 7th Edition
Chapter 4, Problem 34 ↓
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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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Part A - Find the initial voltage across the capacitor For the given circuit (Figure 1), the switch has been at position a for a long time. Find the initial voltage across the capacitor. Assume that Vg = 94.0 V, R1 = 63.0 k̩, R2 = 23.0 k̩, R3 = 45.0 k̩, and C = 84.0 μF. Express your answer to three significant figures and include the appropriate units. Part B - Find the time constant after t = 0 The diagram (Figure 2) represents the original circuit the instant after the switch moves. Find the time constant after t = 0. Assume that R1 = 40.0 k̩, R2 = 27.0 k̩, R3 = 92.0 k̩, and C = 23.0 μF. Express your answer to three significant figures and include the appropriate units. Part C - Find an expression for the capacitor voltage, v(t), for t ≥ 0 Enter an expression for the capacitor voltage v(t) for t ≥ 0. Use the figure in Part B for this part since it shows the circuit after switching. Express your answer as an algebraic expression in terms of R1, R2, R3, Vg, and C. Part D - Find an expression for the current i(t) through resistor R3 for t ≥ 0+ Find an expression for the current i(t) through resistor R3 for t ≥ 0+. Use the figure in Part B for this part since it shows the circuit after switching. Express your answer as a symbolic expression in terms of R1, R2, R3, Vg, and C.

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