Find i(t) and vɖ(t) in the circuit below:
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![### Analysis of RLC Circuit with AC Source
#### AC Voltage Source:
- The voltage source is given by:
\[
v(t) = 60 \cos(3200t)
\]
where \( v(t) \) is the voltage in volts, and \( t \) is the time in seconds. The source is a sinusoidal AC voltage with an amplitude of 60 volts and an angular frequency of 3200 radians per second.
#### Circuit Components:
1. **Resistor (R)**
- Resistance: \( R = 5 \Omega \)
2. **Inductor (L)**
- Inductance: \( L = 0.2 \text{H} \)
3. **Capacitor (C)**
- Capacitance: \( C = 0.1 \text{F} \)
#### Circuit Diagram:
The provided circuit diagram illustrates the series connection of the resistor (R), inductor (L), and capacitor (C), forming an RLC series circuit.
- **Resistor (R):**
- Located at the top of the circuit.
- Marked with \( 5 \Omega \).
- **Inductor (L):**
- Positioned after the resistor in the series.
- Marked with \( 0.2 \text{H} \).
- **Capacitor (C):**
- Positioned next to the inductor.
- Marked with \( 0.1 \text{F} \).
#### Current Direction:
- The current \( i(t) \) is shown flowing in a clockwise direction through the circuit components.
#### Voltage Across the Capacitor:
- The voltage across the capacitor is denoted as \( v_c(t) \), with the positive terminal indicated at the top of the capacitor.
This setup is crucial for analyzing the behavior of the RLC circuit under the influence of the AC voltage source, understanding the reactance of the inductor and capacitor, and how they interact with the resistor over different frequencies defined by the source.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F755354d9-56be-4d3a-9cd7-bb7b08867ede%2F406d427f-ab78-4635-84b7-1a0890d608d9%2F80vly2_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of RLC Circuit with AC Source
#### AC Voltage Source:
- The voltage source is given by:
\[
v(t) = 60 \cos(3200t)
\]
where \( v(t) \) is the voltage in volts, and \( t \) is the time in seconds. The source is a sinusoidal AC voltage with an amplitude of 60 volts and an angular frequency of 3200 radians per second.
#### Circuit Components:
1. **Resistor (R)**
- Resistance: \( R = 5 \Omega \)
2. **Inductor (L)**
- Inductance: \( L = 0.2 \text{H} \)
3. **Capacitor (C)**
- Capacitance: \( C = 0.1 \text{F} \)
#### Circuit Diagram:
The provided circuit diagram illustrates the series connection of the resistor (R), inductor (L), and capacitor (C), forming an RLC series circuit.
- **Resistor (R):**
- Located at the top of the circuit.
- Marked with \( 5 \Omega \).
- **Inductor (L):**
- Positioned after the resistor in the series.
- Marked with \( 0.2 \text{H} \).
- **Capacitor (C):**
- Positioned next to the inductor.
- Marked with \( 0.1 \text{F} \).
#### Current Direction:
- The current \( i(t) \) is shown flowing in a clockwise direction through the circuit components.
#### Voltage Across the Capacitor:
- The voltage across the capacitor is denoted as \( v_c(t) \), with the positive terminal indicated at the top of the capacitor.
This setup is crucial for analyzing the behavior of the RLC circuit under the influence of the AC voltage source, understanding the reactance of the inductor and capacitor, and how they interact with the resistor over different frequencies defined by the source.
Transcribed Image Text:"Find \(i(t)\) and \(v_c(t)\) in the circuit below:"
Note: The image referenced does not contain a graph or diagram. The text is likely part of an educational task or problem statement related to circuit analysis. To solve for the current \(i(t)\) and the voltage across the capacitor \(v_c(t)\) in a given circuit, one would typically need to apply techniques such as Kirchhoff's laws, the Laplace transform, or differential equations, depending on the specifics of the circuit configuration provided in the associated diagram.
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