The circuit shown in the sketch is connected to an ac generator with an rms voltage of 120 V. What value must R have if the rms current in this circuit to approach 1.0 A at high frequency? Answer Units: [Ohms] R 500 ww L Original circuit C₁ 120 V 1000 C₂
The circuit shown in the sketch is connected to an ac generator with an rms voltage of 120 V. What value must R have if the rms current in this circuit to approach 1.0 A at high frequency? Answer Units: [Ohms] R 500 ww L Original circuit C₁ 120 V 1000 C₂
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![### Understanding the Circuit Configuration
The circuit shown in the sketch is connected to an AC generator with an RMS (Root Mean Square) voltage of 120 V.
#### Objective:
Determine the value of the resistor \( R \) such that the RMS current in the circuit approaches 1.0 A at high frequency.
#### Required:
The answer units should be in [Ohms].
### Circuit Diagram Details:
The circuit comprises the following components:
1. An AC generator providing an RMS voltage of 120 V.
2. A resistor \( R \) (whose value is to be determined).
3. A 50-ohm resistor.
4. A 100-ohm resistor.
5. An inductor (denoted as L).
6. Two capacitors (\( C_1 \) and \( C_2 \)).
##### Explanation of the Components:
- **Resistor \( R \)**: This is the variable resistor whose value we aim to determine.
- **50-ohm Resistor and 100-ohm Resistor**: These fixed resistors are part of the network that affects the total impedance of the circuit.
- **Inductor \( L \)** and **Capacitors (\( C_1 \), \( C_2 \))**: These components contribute to the reactive part of the impedance. At high frequencies, the inductive and capacitive reactances influence the circuit behavior significantly.
#### High Frequency Consideration:
At high frequencies:
- The reactance of an inductor (\( X_L = \omega L \)) increases.
- The reactance of a capacitor (\( X_C = 1/(\omega C) \)) decreases.
Given the target current of 1.0 A RMS, the total impedance \( Z \) of the circuit must satisfy Ohm’s Law:
\[ V_{RMS} = I_{RMS} \cdot Z \]
Substituting the known values:
\[ 120 \text{ V} = 1.0 \text{ A} \cdot Z \]
Thus, the impedance \( Z \) must be 120 ohms. The value of \( R \) must be determined to achieve this total impedance considering the influence of other resistors and reactive components.
### Conclusion:
By analyzing how the impedance of inductors and capacitors change with frequency, and taking into account the circuit’s configuration, we can use Ohm's](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F203b58df-0ca9-47a6-a660-754b46a1e0bb%2Fd34114a7-fc9d-426d-a839-236c96f4ad42%2Feaukfqi_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Circuit Configuration
The circuit shown in the sketch is connected to an AC generator with an RMS (Root Mean Square) voltage of 120 V.
#### Objective:
Determine the value of the resistor \( R \) such that the RMS current in the circuit approaches 1.0 A at high frequency.
#### Required:
The answer units should be in [Ohms].
### Circuit Diagram Details:
The circuit comprises the following components:
1. An AC generator providing an RMS voltage of 120 V.
2. A resistor \( R \) (whose value is to be determined).
3. A 50-ohm resistor.
4. A 100-ohm resistor.
5. An inductor (denoted as L).
6. Two capacitors (\( C_1 \) and \( C_2 \)).
##### Explanation of the Components:
- **Resistor \( R \)**: This is the variable resistor whose value we aim to determine.
- **50-ohm Resistor and 100-ohm Resistor**: These fixed resistors are part of the network that affects the total impedance of the circuit.
- **Inductor \( L \)** and **Capacitors (\( C_1 \), \( C_2 \))**: These components contribute to the reactive part of the impedance. At high frequencies, the inductive and capacitive reactances influence the circuit behavior significantly.
#### High Frequency Consideration:
At high frequencies:
- The reactance of an inductor (\( X_L = \omega L \)) increases.
- The reactance of a capacitor (\( X_C = 1/(\omega C) \)) decreases.
Given the target current of 1.0 A RMS, the total impedance \( Z \) of the circuit must satisfy Ohm’s Law:
\[ V_{RMS} = I_{RMS} \cdot Z \]
Substituting the known values:
\[ 120 \text{ V} = 1.0 \text{ A} \cdot Z \]
Thus, the impedance \( Z \) must be 120 ohms. The value of \( R \) must be determined to achieve this total impedance considering the influence of other resistors and reactive components.
### Conclusion:
By analyzing how the impedance of inductors and capacitors change with frequency, and taking into account the circuit’s configuration, we can use Ohm's
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