5. Find the impedance Z, shown in the figure below at a frequency of 400 H. 10 mH 2Ω 10 μF
5. Find the impedance Z, shown in the figure below at a frequency of 400 H. 10 mH 2Ω 10 μF
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Please answer question 5 with details on how to do it. Make handwriting legible please. Thank you.
![**Problem 5: Calculating Impedance in an RLC Circuit**
Objective: Determine the impedance \( Z \) in the circuit diagram provided at a frequency of 400 Hz.
### Circuit Components:
1. **Inductor**:
- A 10 mH inductor, located on the left side of the circuit.
2. **Resistors**:
- One 2 Ω resistor, connected in series with the inductor.
- One 1 Ω resistor, connected in parallel with the series combination of the inductor and the 2 Ω resistor.
3. **Capacitor**:
- A 10 μF capacitor, connected in parallel with the 1 Ω resistor.
### Circuit Description:
The circuit is a combination of series and parallel components. The inductor (10 mH) is in series with a 2 Ω resistor. This series combination is in parallel with another branch consisting of a 1 Ω resistor in parallel with a 10 μF capacitor. The task is to find the overall impedance (\( Z \)) seen from the terminals indicated.
### Calculations:
To find the impedance \( Z \) at a frequency of 400 Hz, the following steps should be carried out:
1. **Inductive Reactance** (\( X_L \)):
\[
X_L = 2\pi f L = 2\pi (400) (10 \times 10^{-3}) \, \Omega
\]
2. **Capacitive Reactance** (\( X_C \)):
\[
X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi (400) (10 \times 10^{-6})} \, \Omega
\]
3. **Series Combination**:
- Calculate the impedance of the inductor and the 2 Ω resistor in series.
4. **Parallel Combination**:
- Find the equivalent impedance of the parallel branches consisting of the series inductor-resistor combination and the 1 Ω resistor with the capacitor.
By following these steps, you will determine the overall impedance \( Z \) of the circuit at the specified frequency.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1296c196-158c-4a2c-9587-82b5996e9fed%2F74e1c823-8e4f-44a3-bd03-c75e9d06055e%2F0qwumgi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5: Calculating Impedance in an RLC Circuit**
Objective: Determine the impedance \( Z \) in the circuit diagram provided at a frequency of 400 Hz.
### Circuit Components:
1. **Inductor**:
- A 10 mH inductor, located on the left side of the circuit.
2. **Resistors**:
- One 2 Ω resistor, connected in series with the inductor.
- One 1 Ω resistor, connected in parallel with the series combination of the inductor and the 2 Ω resistor.
3. **Capacitor**:
- A 10 μF capacitor, connected in parallel with the 1 Ω resistor.
### Circuit Description:
The circuit is a combination of series and parallel components. The inductor (10 mH) is in series with a 2 Ω resistor. This series combination is in parallel with another branch consisting of a 1 Ω resistor in parallel with a 10 μF capacitor. The task is to find the overall impedance (\( Z \)) seen from the terminals indicated.
### Calculations:
To find the impedance \( Z \) at a frequency of 400 Hz, the following steps should be carried out:
1. **Inductive Reactance** (\( X_L \)):
\[
X_L = 2\pi f L = 2\pi (400) (10 \times 10^{-3}) \, \Omega
\]
2. **Capacitive Reactance** (\( X_C \)):
\[
X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi (400) (10 \times 10^{-6})} \, \Omega
\]
3. **Series Combination**:
- Calculate the impedance of the inductor and the 2 Ω resistor in series.
4. **Parallel Combination**:
- Find the equivalent impedance of the parallel branches consisting of the series inductor-resistor combination and the 1 Ω resistor with the capacitor.
By following these steps, you will determine the overall impedance \( Z \) of the circuit at the specified frequency.
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