Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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**Problem 8.28: Find \( v_S(t) \) in the circuit in Fig. P8.28.**

**Figure P8.28 Description:**

This figure represents an electrical circuit composed of:

- A voltage source labeled \( v_S(t) \).
- A resistor with a resistance of \( 40 \, \Omega \), represented by a zigzag line.
- A capacitor with a capacitance of \( 25 \, \mu F \), depicted by two parallel lines with a gap between them, indicating the capacitor's plates.
- The voltage across the capacitor is given by the expression \( v_C(t) = 80 \cos (1000t - 60^\circ) \, \text{V} \).

The components are connected in series to form a closed loop, with the polarity of the voltage source and the capacitor indicated by plus and minus signs.
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Transcribed Image Text:**Problem 8.28: Find \( v_S(t) \) in the circuit in Fig. P8.28.** **Figure P8.28 Description:** This figure represents an electrical circuit composed of: - A voltage source labeled \( v_S(t) \). - A resistor with a resistance of \( 40 \, \Omega \), represented by a zigzag line. - A capacitor with a capacitance of \( 25 \, \mu F \), depicted by two parallel lines with a gap between them, indicating the capacitor's plates. - The voltage across the capacitor is given by the expression \( v_C(t) = 80 \cos (1000t - 60^\circ) \, \text{V} \). The components are connected in series to form a closed loop, with the polarity of the voltage source and the capacitor indicated by plus and minus signs.
Expert Solution
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Step 1

Based on given circuit is Series circuit. In series circuits current is same in all elements but voltage is distributed based on their Impedance values.

Here vc(t) is given as

     vc(t)=80 cos (1000t-60°) V

     w=1000Xc=1jwc     =1j1000×25×10-6     = 1000j25=40Xc= -j40

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