4. Determine the impedance of the circuit of Figure 4.4 at frequencies of 1 kHz, 20 kHz and 1 MHz. 390 Figure 4.4 33 nF 22 mH 680 www
4. Determine the impedance of the circuit of Figure 4.4 at frequencies of 1 kHz, 20 kHz and 1 MHz. 390 Figure 4.4 33 nF 22 mH 680 www
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Determine the impedance of the circuit of Figure 4.4 at frequencies of 1 kHz, 20 kHz and 1 MHz.
NOTE: Resistance values are in Ohms
![### Example Problem: Frequency Analysis of LCR Circuit
#### Problem Statement:
Determine the impedance of the circuit of Figure 4.4 at frequencies of 1 kHz, 20 kHz, and 1 MHz.
#### Figure 4.4:
The circuit consists of a series-parallel configuration with the following components:
- A 22 mH inductor in parallel with a series combination of a 33 nF capacitor and a 680-ohm resistor.
- The combination described above is in series with a 390-ohm resistor.
#### Step-by-step Solution:
To determine the impedance of the given circuit at different frequencies, we need to calculate the individual impedances of the inductor, capacitor, and resistors at each specified frequency. The impedance for inductors, capacitors, and resistors can be calculated as follows:
1. **Impedance of an Inductor (L):**
\[
Z_L = j\omega L
\]
Where:
- \( j \) is the imaginary unit,
- \( \omega = 2\pi f \) is the angular frequency,
- \( L \) is the inductance.
2. **Impedance of a Capacitor (C):**
\[
Z_C = \frac{1}{j\omega C}
\]
Where:
- \( C \) is the capacitance.
3. **Impedance of a Resistor (R):**
\[
Z_R = R
\]
Let's denote the inductance as \( L = 22 \text{ mH} \), the capacitance as \( C = 33 \text{ nF} \), and the resistances as \(R1 = 390 \Omega \) and \( R2 = 680 \Omega \).
**Determining Impedance at Different Frequencies**:
- **At 1 kHz (1000 Hz):**
\[
\omega = 2\pi \times 1000 \text{ rad/s}
\]
\[
Z_L = j\omega L = j \cdot 2\pi \cdot 1000 \cdot 22 \times 10^{-3} \text{ H}
\]
\[
Z_C = \frac{1}{j\omega C} = \frac{1}{j \cdot](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5842debd-c7e0-436d-83d9-66a4971dddbf%2Fd7761202-e7da-4587-9e0d-e63a11ab7eb9%2Fyeq0qna_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem: Frequency Analysis of LCR Circuit
#### Problem Statement:
Determine the impedance of the circuit of Figure 4.4 at frequencies of 1 kHz, 20 kHz, and 1 MHz.
#### Figure 4.4:
The circuit consists of a series-parallel configuration with the following components:
- A 22 mH inductor in parallel with a series combination of a 33 nF capacitor and a 680-ohm resistor.
- The combination described above is in series with a 390-ohm resistor.
#### Step-by-step Solution:
To determine the impedance of the given circuit at different frequencies, we need to calculate the individual impedances of the inductor, capacitor, and resistors at each specified frequency. The impedance for inductors, capacitors, and resistors can be calculated as follows:
1. **Impedance of an Inductor (L):**
\[
Z_L = j\omega L
\]
Where:
- \( j \) is the imaginary unit,
- \( \omega = 2\pi f \) is the angular frequency,
- \( L \) is the inductance.
2. **Impedance of a Capacitor (C):**
\[
Z_C = \frac{1}{j\omega C}
\]
Where:
- \( C \) is the capacitance.
3. **Impedance of a Resistor (R):**
\[
Z_R = R
\]
Let's denote the inductance as \( L = 22 \text{ mH} \), the capacitance as \( C = 33 \text{ nF} \), and the resistances as \(R1 = 390 \Omega \) and \( R2 = 680 \Omega \).
**Determining Impedance at Different Frequencies**:
- **At 1 kHz (1000 Hz):**
\[
\omega = 2\pi \times 1000 \text{ rad/s}
\]
\[
Z_L = j\omega L = j \cdot 2\pi \cdot 1000 \cdot 22 \times 10^{-3} \text{ H}
\]
\[
Z_C = \frac{1}{j\omega C} = \frac{1}{j \cdot
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