For the Wien bridge shown in figure 1:9, R₂ = R3 = 30 kQ, R₁ = 1 kQ and C₂ = C3 = 1nF. Determine, the value of resistance R₁, and the frequency of the bridge when bridge is balanced. Figure 1: 9
For the Wien bridge shown in figure 1:9, R₂ = R3 = 30 kQ, R₁ = 1 kQ and C₂ = C3 = 1nF. Determine, the value of resistance R₁, and the frequency of the bridge when bridge is balanced. Figure 1: 9
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![For the Wien bridge shown in Figure 1:9, \( R_2 = R_3 = 30 \, \text{k}\Omega \), \( R_4 = 1 \, \text{k}\Omega \), and \( C_2 = C_3 = 1 \, \text{nF} \).
Determine the value of resistance \( R_1 \), and the frequency of the bridge when the bridge is balanced.
**Diagram Explanation:**
The diagram depicts a Wien bridge circuit. It includes the following components:
- **Resistors:**
- \( R_1 \) is adjustable.
- \( R_2 \) and \( R_3 \) are both 30 kΩ.
- \( R_4 \) is 1 kΩ.
- **Capacitors:**
- \( C_2 \) and \( C_3 \) are both 1 nF.
The bridge is structured in a diamond shape with a source of electromotive force (ε) connected to the circuit. Resistors and capacitors are arranged in alternating branches to create a balance condition at a specific frequency.
**Instructions:**
To find the value of \( R_1 \) and the frequency at which the bridge is balanced, use the standard Wien bridge balance condition:
\[ R_1 \cdot C_2 = R_4 \cdot C_3 \]
The frequency \( f \) at which the bridge is balanced can be computed using:
\[ f = \frac{1}{2\pi \sqrt{R_1 \cdot R_4 \cdot C_2 \cdot C_3}} \]
Inserting the given values into these equations will solve for \( R_1 \) and the bridge's resonant frequency.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79e93c14-ca8c-41ff-9995-d899a7d01441%2Fd6f2ed0e-754d-412f-8f4c-9daa81a50045%2F4kfqso_processed.png&w=3840&q=75)
Transcribed Image Text:For the Wien bridge shown in Figure 1:9, \( R_2 = R_3 = 30 \, \text{k}\Omega \), \( R_4 = 1 \, \text{k}\Omega \), and \( C_2 = C_3 = 1 \, \text{nF} \).
Determine the value of resistance \( R_1 \), and the frequency of the bridge when the bridge is balanced.
**Diagram Explanation:**
The diagram depicts a Wien bridge circuit. It includes the following components:
- **Resistors:**
- \( R_1 \) is adjustable.
- \( R_2 \) and \( R_3 \) are both 30 kΩ.
- \( R_4 \) is 1 kΩ.
- **Capacitors:**
- \( C_2 \) and \( C_3 \) are both 1 nF.
The bridge is structured in a diamond shape with a source of electromotive force (ε) connected to the circuit. Resistors and capacitors are arranged in alternating branches to create a balance condition at a specific frequency.
**Instructions:**
To find the value of \( R_1 \) and the frequency at which the bridge is balanced, use the standard Wien bridge balance condition:
\[ R_1 \cdot C_2 = R_4 \cdot C_3 \]
The frequency \( f \) at which the bridge is balanced can be computed using:
\[ f = \frac{1}{2\pi \sqrt{R_1 \cdot R_4 \cdot C_2 \cdot C_3}} \]
Inserting the given values into these equations will solve for \( R_1 \) and the bridge's resonant frequency.
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