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The figure shows a driven RLC circuit that contains two identical capacitors and two switches. The emf amplitude is set at 12.4 V, and the driving frequency is set at 62.1 Hz. With both switches open, the current leads the emf by 30.2°. With switch S1 closed and switch S2 still open, the emf leads the current by 15.4°. With both switches closed, the current amplitude is 449 mA. What are (a) R, (b) C, and (c) L?

The figure shows a driven RLC circuit that contains two identical capacitors and two switches. The emf amplitude is set at 12.4 V, and the driving frequency is set at 62.1 Hz. With both switches open, the current leads the emf by 30.2°. With switch S1 closed and switch S2 still open, the emf leads the current by 15.4°. With both switches closed, the current amplitude is 449 mA. What are (a) R, (b) C, and (c) L?

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The figure shows a driven RLC circuit that contains two identical capacitors and two switches. The emf amplitude is set at 12.4 V, and the driving frequency is set at 62.1 Hz. With both switches open, the current leads the emf by 30.2°. With switch S1 closed and switch S2 still open, the emf leads the current by 15.4°. With both switches closed, the current amplitude is 449 mA. What are (a) R, (b) C, and (c) L?

The image illustrates a schematic diagram of an LC circuit with additional components designed to demonstrate resonance and filtering principles. ### Circuit Components: 1. **Capacitors (C)**: There are two capacitors in the circuit, one located to the left of the AC source and another to the right, both marked with a 'C'. Capacitors store electrical energy and affect the impedance of the circuit. 2. **Inductor (L)**: The inductor, marked 'L', is positioned above the AC source. It stores energy in a magnetic field when electrical current passes through it and is responsible for creating inductive reactance. 3. **Resistor (R)**: The resistor, denoted by 'R', is placed on the right side of the circuit between the capacitor and switch \( S_2 \). It limits the flow of electric current and dissipates energy in the form of heat. 4. **AC Source**: Located at the bottom of the circuit, it provides the alternating current needed to energize the circuit and facilitate analysis of resonant behavior. 5. **Switches (S1 and S2)**: The switches, labeled \( S_1 \) and \( S_2 \), are placed on either side of the circuit. They allow control over the current flow, enabling the circuit to be opened or closed as needed for experimentation or demonstration. ### Circuit Configuration: - The arrangement shows a typical LC bandpass or band-stop filter structure, depending on the specific component values and configuration. - This type of circuit is used in various applications, including tuning radios to select specific frequencies and in electronic signal processing. ### Functionality: - When the switches \( S_1 \) and \( S_2 \) are closed, the circuit becomes active, allowing current to flow. - The interaction between the inductance \( L \) and capacitance \( C \) causes the circuit to exhibit resonant properties at a particular frequency, determined by the formula \( f = \frac{1}{2\pi\sqrt{LC}} \). - By adjusting \( L \), \( C \), or \( R \), the circuit's resonant frequency and bandwidth can be modified, thus affecting its filtering characteristics. This circuit's versatility makes it a fundamental concept in electronics and electrical engineering, essential for developing skills in circuit design and analysis.
Transcribed Image Text:The image illustrates a schematic diagram of an LC circuit with additional components designed to demonstrate resonance and filtering principles. ### Circuit Components: 1. **Capacitors (C)**: There are two capacitors in the circuit, one located to the left of the AC source and another to the right, both marked with a 'C'. Capacitors store electrical energy and affect the impedance of the circuit. 2. **Inductor (L)**: The inductor, marked 'L', is positioned above the AC source. It stores energy in a magnetic field when electrical current passes through it and is responsible for creating inductive reactance. 3. **Resistor (R)**: The resistor, denoted by 'R', is placed on the right side of the circuit between the capacitor and switch \( S_2 \). It limits the flow of electric current and dissipates energy in the form of heat. 4. **AC Source**: Located at the bottom of the circuit, it provides the alternating current needed to energize the circuit and facilitate analysis of resonant behavior. 5. **Switches (S1 and S2)**: The switches, labeled \( S_1 \) and \( S_2 \), are placed on either side of the circuit. They allow control over the current flow, enabling the circuit to be opened or closed as needed for experimentation or demonstration. ### Circuit Configuration: - The arrangement shows a typical LC bandpass or band-stop filter structure, depending on the specific component values and configuration. - This type of circuit is used in various applications, including tuning radios to select specific frequencies and in electronic signal processing. ### Functionality: - When the switches \( S_1 \) and \( S_2 \) are closed, the circuit becomes active, allowing current to flow. - The interaction between the inductance \( L \) and capacitance \( C \) causes the circuit to exhibit resonant properties at a particular frequency, determined by the formula \( f = \frac{1}{2\pi\sqrt{LC}} \). - By adjusting \( L \), \( C \), or \( R \), the circuit's resonant frequency and bandwidth can be modified, thus affecting its filtering characteristics. This circuit's versatility makes it a fundamental concept in electronics and electrical engineering, essential for developing skills in circuit design and analysis.
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