3. For the circuit shown, use the voltage divider rule to find the phasor Vo. Ve=50/0° V R₁ 10 Ω с HH -50 -200 V₂ jan
3. For the circuit shown, use the voltage divider rule to find the phasor Vo. Ve=50/0° V R₁ 10 Ω с HH -50 -200 V₂ jan
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![**Homework Problem: Phasor Analysis using the Voltage Divider Rule**
### Problem Statement
3. For the circuit shown, use the voltage divider rule to find the phasor \( V_o \).
### Circuit Description
The given circuit includes:
- A voltage source \( V_s = 50\angle 0^\circ V \)
- Resistor \( R_1 \) with a resistance of 10 Ω
- Capacitor \( C \) with an impedance of -5 Ω
- Resistor \( R_2 \) with a resistance of 20 Ω
- Inductor \( L \) with an impedance of 18 Ω
### Circuit Diagram
The circuit is as follows:
- The voltage source \( V_s \) is connected in series.
- Resistor \( R_1 \) and Capacitor \( C \) are connected in parallel with respect to each other.
- This parallel combination is then connected in series with Resistor \( R_2 \) and Inductor \( L \) (which are also in series with each other).
### Analysis Objective
Use the voltage divider rule to determine the phasor voltage \( V_o \) across the series combination of Resistor \( R_2 \) and Inductor \( L \).
### Steps for Solution:
1. **Combine the Parallel Impedance:**
- The combined impedance \( Z_{parallel} \) of \( R_1 \) and \( C \) in parallel is calculated as:
\[
Z_{parallel} = \frac{Z_{R_1} \cdot Z_C}{Z_{R_1} + Z_C}
\]
Where \( Z_{R_1} = 10 \) Ω and \( Z_C = -5 \) Ω.
2. **Calculate Total Impedance of the Circuit:**
- The total impedance (\( Z_{total} \)) is found by adding the impedance of the series components:
\[
Z_{total} = Z_{parallel} + Z_{R_2} + Z_L
\]
Where \( Z_{R_2} = 20 \) Ω and \( Z_L = 18 \) Ω.
3. **Apply Voltage Divider Rule:**
- Use the voltage divider rule to find the voltage across the series components:
\[
V_o = V_s \cdot \frac{Z_{R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdaad9e7e-1f14-44d5-98ac-51623b651f9b%2F65045576-088a-4d29-8f77-b85befaf3105%2Fwktmz3_processed.png&w=3840&q=75)
Transcribed Image Text:**Homework Problem: Phasor Analysis using the Voltage Divider Rule**
### Problem Statement
3. For the circuit shown, use the voltage divider rule to find the phasor \( V_o \).
### Circuit Description
The given circuit includes:
- A voltage source \( V_s = 50\angle 0^\circ V \)
- Resistor \( R_1 \) with a resistance of 10 Ω
- Capacitor \( C \) with an impedance of -5 Ω
- Resistor \( R_2 \) with a resistance of 20 Ω
- Inductor \( L \) with an impedance of 18 Ω
### Circuit Diagram
The circuit is as follows:
- The voltage source \( V_s \) is connected in series.
- Resistor \( R_1 \) and Capacitor \( C \) are connected in parallel with respect to each other.
- This parallel combination is then connected in series with Resistor \( R_2 \) and Inductor \( L \) (which are also in series with each other).
### Analysis Objective
Use the voltage divider rule to determine the phasor voltage \( V_o \) across the series combination of Resistor \( R_2 \) and Inductor \( L \).
### Steps for Solution:
1. **Combine the Parallel Impedance:**
- The combined impedance \( Z_{parallel} \) of \( R_1 \) and \( C \) in parallel is calculated as:
\[
Z_{parallel} = \frac{Z_{R_1} \cdot Z_C}{Z_{R_1} + Z_C}
\]
Where \( Z_{R_1} = 10 \) Ω and \( Z_C = -5 \) Ω.
2. **Calculate Total Impedance of the Circuit:**
- The total impedance (\( Z_{total} \)) is found by adding the impedance of the series components:
\[
Z_{total} = Z_{parallel} + Z_{R_2} + Z_L
\]
Where \( Z_{R_2} = 20 \) Ω and \( Z_L = 18 \) Ω.
3. **Apply Voltage Divider Rule:**
- Use the voltage divider rule to find the voltage across the series components:
\[
V_o = V_s \cdot \frac{Z_{R
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