Q4) Answer question related to circuit giver Given vs(t) = 15 cos(100t) V a) Write vs(t) in phasor form b) In Figure 4a, what is Z₁? c) In Figure 4a, what is Zc? US(1) 10 0 50 mH 150 Συ(0) Figure 4a Z₁ 42(1) 1mF
Q4) Answer question related to circuit giver Given vs(t) = 15 cos(100t) V a) Write vs(t) in phasor form b) In Figure 4a, what is Z₁? c) In Figure 4a, what is Zc? US(1) 10 0 50 mH 150 Συ(0) Figure 4a Z₁ 42(1) 1mF
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![**Circuit Analysis Problem:**
Given \[ v_{S}(t) = 15 \cos (100t) \, V \]
### Questions:
a) Write \( v_{S}(t) \) in phasor form.
b) In Figure 4a, what is \( Z_L \)?
c) In Figure 4a, what is \( Z_C \)?
### Explanation of Figures:
**Figure 4a:**
This figure represents an AC circuit consisting of:
- A voltage source \( v_{S}(t) \) with a voltage of \( 15 \cos(100t) \, V \).
- A series resistor of 10 ohms (Ω).
- An inductor of 50 millihenries (mH).
- A resistor of 15 ohms (Ω) in parallel with the combination of the 50 mH inductor.
- A capacitor of 1 millifarad (mF) in parallel with the resistor-inductor combination.
### Analyzing Figure 4a Components:
1. **Inductor (\( Z_L \)) Calculation:**
- Inductor \( Z_L \) can be found using \( Z_L = j \omega L \), where \( \omega = 100 \, rad/s \) and \( L = 50 \, mH \).
2. **Capacitor (\( Z_C \)) Calculation:**
- Capacitor \( Z_C \) can be found using \( Z_C = \dfrac{1}{j \omega C} \), where \( \omega = 100 \, rad/s \) and \( C = 1 \, mF \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2Ff02a059a-108c-4a73-8588-dd3d950a0d8e%2Fp9ulx7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Circuit Analysis Problem:**
Given \[ v_{S}(t) = 15 \cos (100t) \, V \]
### Questions:
a) Write \( v_{S}(t) \) in phasor form.
b) In Figure 4a, what is \( Z_L \)?
c) In Figure 4a, what is \( Z_C \)?
### Explanation of Figures:
**Figure 4a:**
This figure represents an AC circuit consisting of:
- A voltage source \( v_{S}(t) \) with a voltage of \( 15 \cos(100t) \, V \).
- A series resistor of 10 ohms (Ω).
- An inductor of 50 millihenries (mH).
- A resistor of 15 ohms (Ω) in parallel with the combination of the 50 mH inductor.
- A capacitor of 1 millifarad (mF) in parallel with the resistor-inductor combination.
### Analyzing Figure 4a Components:
1. **Inductor (\( Z_L \)) Calculation:**
- Inductor \( Z_L \) can be found using \( Z_L = j \omega L \), where \( \omega = 100 \, rad/s \) and \( L = 50 \, mH \).
2. **Capacitor (\( Z_C \)) Calculation:**
- Capacitor \( Z_C \) can be found using \( Z_C = \dfrac{1}{j \omega C} \), where \( \omega = 100 \, rad/s \) and \( C = 1 \, mF \).
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