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Assume that the switch in the circuit of Fig. P7.51 has been in position a for a long time and that at 1 = 0 it is moved to position b. Find (a) vɖ0*); (b) 7 for t > 0; (c) vď∞); (d) i(0*); (e) vc, t z 0; and (f) i, t ² 0+.

Assume that the switch in the circuit of Fig. P7.51 has been in position a for a long time and that at 1 = 0 it is moved to position b. Find (a) vɖ0*); (b) 7 for t > 0; (c) vď∞); (d) i(0*); (e) vc, t z 0; and (f) i, t ² 0+.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Solve with the general solution equation please
The image displays a circuit diagram labeled "Figure P7.51." The circuit consists of the following components: 1. **Voltage Sources:** - A 50 V voltage source at the top. - A 30 V voltage source at the bottom. 2. **Resistors:** - A 400 Ω resistor connected to node 'a'. - A 20 Ω resistor connected in series with the 30 V source. - A 5 Ω resistor positioned horizontally between the two vertical branches. 3. **Capacitor:** - A capacitor with a capacitance of 25 mF. - The capacitor is placed between the two main vertical branches of the circuit. - It is labeled with a voltage across it \( v_c \) and a current \( i_c \) flowing through it. 4. **Switch:** - A switch is depicted between nodes 'a' and 'b'. - The switch position is shown as open, and marked with \( t = 0 \), indicating the moment the switch changes state. The circuit illustrates a typical RC (resistor-capacitor) network with a time-dependent switch, which is commonly used in transient response analysis. The switch alters the connection in the circuit at \( t = 0 \), which might be analyzed to study the charging or discharging behavior of the capacitor.
Transcribed Image Text:The image displays a circuit diagram labeled "Figure P7.51." The circuit consists of the following components: 1. **Voltage Sources:** - A 50 V voltage source at the top. - A 30 V voltage source at the bottom. 2. **Resistors:** - A 400 Ω resistor connected to node 'a'. - A 20 Ω resistor connected in series with the 30 V source. - A 5 Ω resistor positioned horizontally between the two vertical branches. 3. **Capacitor:** - A capacitor with a capacitance of 25 mF. - The capacitor is placed between the two main vertical branches of the circuit. - It is labeled with a voltage across it \( v_c \) and a current \( i_c \) flowing through it. 4. **Switch:** - A switch is depicted between nodes 'a' and 'b'. - The switch position is shown as open, and marked with \( t = 0 \), indicating the moment the switch changes state. The circuit illustrates a typical RC (resistor-capacitor) network with a time-dependent switch, which is commonly used in transient response analysis. The switch alters the connection in the circuit at \( t = 0 \), which might be analyzed to study the charging or discharging behavior of the capacitor.
**7.51** Assume that the switch in the circuit of Fig. P7.51 has been in position a for a long time and that at \( t = 0 \) it is moved to position b. Find (a) \( v_c(0^-); \) (b) \( \tau \) for \( t > 0; \) (c) \( v_c(\infty); \) (d) \( i(0^+); \) (e) \( v_c, t \geq 0; \) and (f) \( i, t \geq 0^+. \) **Explanation:** This problem asks for an analysis of a circuit when a switch is moved from one position to another at time \( t = 0 \). The parameters requested (a through f) typically involve calculating initial and final values of voltages and currents, time constants, and expressions for values over time. **Diagrams:** Unfortunately, the image only shows a partial section of a graph or circuit diagram. It appears there might be circuit components involved that influence the analysis. To fully understand or explain the circuit behavior, a complete view of the diagram along with any elements like resistors, capacitors, inductors, or sources is needed.
Transcribed Image Text:**7.51** Assume that the switch in the circuit of Fig. P7.51 has been in position a for a long time and that at \( t = 0 \) it is moved to position b. Find (a) \( v_c(0^-); \) (b) \( \tau \) for \( t > 0; \) (c) \( v_c(\infty); \) (d) \( i(0^+); \) (e) \( v_c, t \geq 0; \) and (f) \( i, t \geq 0^+. \) **Explanation:** This problem asks for an analysis of a circuit when a switch is moved from one position to another at time \( t = 0 \). The parameters requested (a through f) typically involve calculating initial and final values of voltages and currents, time constants, and expressions for values over time. **Diagrams:** Unfortunately, the image only shows a partial section of a graph or circuit diagram. It appears there might be circuit components involved that influence the analysis. To fully understand or explain the circuit behavior, a complete view of the diagram along with any elements like resistors, capacitors, inductors, or sources is needed.
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