V(t) = 10 cos(100t) 10 Ω ww →i(t) 2 mH m 10 mF gure 1: Use the circuit in Figure 1 to answer the following questions: Transform the circuit to the frequency domain. What are the frequency domain quantities, V, ZR, ZL and Zc? Apply KVL to determine the phasor current, I, flowing in the series circuit. Determine the phasor capacitor voltage, Vc.

Introductory Circuit Analysis (13th Edition)
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**Figure 1:**

Circuit Description:
- The circuit consists of a series combination of a resistor, inductor, and capacitor.
- Components:
  - A 10 Ω resistor.
  - A 2 mH inductor.
  - A 10 mF capacitor.
  - The voltage source is given as \( V(t) = 10 \cos(100t) \).
  - The current \( i(t) \) flows through the circuit.

**Tasks:**
1. Use the circuit in Figure 1 to answer the following questions:
   a) Transform the circuit to the frequency domain. Determine the frequency domain quantities: \( V \), \( Z_R \), \( Z_L \), and \( Z_C \).
   
   b) Apply Kirchhoff's Voltage Law (KVL) to determine the phasor current, \( I \), flowing in the series circuit.
   
   c) Determine the phasor capacitor voltage, \( V_C \).
   
   d) Determine the phasor inductor voltage, \( V_L \).
   
   e) Identify which variable is leading — \( I_L \) or \( V_L \)? Determine the phase angle.
   
   f) Transform the current and voltage back to the time domain to obtain \( i(t) \), \( v_C(t) \), and \( v_L(t) \).
Transcribed Image Text:**Figure 1:** Circuit Description: - The circuit consists of a series combination of a resistor, inductor, and capacitor. - Components: - A 10 Ω resistor. - A 2 mH inductor. - A 10 mF capacitor. - The voltage source is given as \( V(t) = 10 \cos(100t) \). - The current \( i(t) \) flows through the circuit. **Tasks:** 1. Use the circuit in Figure 1 to answer the following questions: a) Transform the circuit to the frequency domain. Determine the frequency domain quantities: \( V \), \( Z_R \), \( Z_L \), and \( Z_C \). b) Apply Kirchhoff's Voltage Law (KVL) to determine the phasor current, \( I \), flowing in the series circuit. c) Determine the phasor capacitor voltage, \( V_C \). d) Determine the phasor inductor voltage, \( V_L \). e) Identify which variable is leading — \( I_L \) or \( V_L \)? Determine the phase angle. f) Transform the current and voltage back to the time domain to obtain \( i(t) \), \( v_C(t) \), and \( v_L(t) \).
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d) Determine the phasor inductor voltage, VL.

e) Which variable is leading - IL or V₁? By what angle?

f) Transform the current and voltage back to the time domain to get i(t) and vc(t) and VL(t).

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