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The rms current in an RLC circuit depends on the frequency of the power source as shown below. It reaches its maximum value at fo = 79.6 Hz. Find the rms voltage applied to the circuit if R = 40 N, C = 40 µF, and L = 100 mH. 2.5 2.0 1.5 1.0 0.5 250 50 Frequency (Hertz) 100 150 200 Current (Amps)

The rms current in an RLC circuit depends on the frequency of the power source as shown below. It reaches its maximum value at fo = 79.6 Hz. Find the rms voltage applied to the circuit if R = 40 N, C = 40 µF, and L = 100 mH. 2.5 2.0 1.5 1.0 0.5 250 50 Frequency (Hertz) 100 150 200 Current (Amps)

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### RMS Current in an RLC Circuit The root mean square (RMS) current in a series RLC circuit varies with the frequency of the AC power source as illustrated in the graph below. The peak current is reached at a resonant frequency, \( f_0 \), equal to 79.6 Hz. Your task is to determine the RMS voltage applied to this circuit with given component values: \( R \) = 40 Ω, \( C \) = 40 µF, and \( L \) = 100 mH. The graph provided shows the relationship between Current (Amps) and Frequency (Hertz): - **Vertical Axis (Y-axis):** Represents the Current in Amperes (Amps), ranging from 0 to 2.5 Amps. - **Horizontal Axis (X-axis):** Represents the Frequency in Hertz (Hz), ranging from 0 to 250 Hz. - **Peak Point:** The graph indicates that the peak current value, labeled as \( f_0 \), occurs at 79.6 Hz with a maximum current approximately around 2.0 Amps. **Given Parameters:** - Resistor, \( R \) : 40 Ω - Capacitor, \( C \) : 40 µF - Inductor, \( L \) : 100 mH **Graph Analysis:** - The plot shows a sharp peak at the resonant frequency where the current is at its maximum. - The current decreases significantly when the frequency moves away from the resonant frequency, indicating the resonance behavior of the RLC circuit. **Problem Statement:** Calculate the RMS voltage applied to the circuit. **Interactive Element:** - Input Box: "The voltage, \( V \) = _____." - Units Drop-down: "Select an answer." --- This educational content helps in understanding the concept of resonance in an RLC circuit and how the components interact with the applied frequency to affect the RMS current. By analyzing the graph, students can visualize how the current changes with different frequencies and use given values to calculate key parameters such as the RMS voltage.
Transcribed Image Text:### RMS Current in an RLC Circuit The root mean square (RMS) current in a series RLC circuit varies with the frequency of the AC power source as illustrated in the graph below. The peak current is reached at a resonant frequency, \( f_0 \), equal to 79.6 Hz. Your task is to determine the RMS voltage applied to this circuit with given component values: \( R \) = 40 Ω, \( C \) = 40 µF, and \( L \) = 100 mH. The graph provided shows the relationship between Current (Amps) and Frequency (Hertz): - **Vertical Axis (Y-axis):** Represents the Current in Amperes (Amps), ranging from 0 to 2.5 Amps. - **Horizontal Axis (X-axis):** Represents the Frequency in Hertz (Hz), ranging from 0 to 250 Hz. - **Peak Point:** The graph indicates that the peak current value, labeled as \( f_0 \), occurs at 79.6 Hz with a maximum current approximately around 2.0 Amps. **Given Parameters:** - Resistor, \( R \) : 40 Ω - Capacitor, \( C \) : 40 µF - Inductor, \( L \) : 100 mH **Graph Analysis:** - The plot shows a sharp peak at the resonant frequency where the current is at its maximum. - The current decreases significantly when the frequency moves away from the resonant frequency, indicating the resonance behavior of the RLC circuit. **Problem Statement:** Calculate the RMS voltage applied to the circuit. **Interactive Element:** - Input Box: "The voltage, \( V \) = _____." - Units Drop-down: "Select an answer." --- This educational content helps in understanding the concept of resonance in an RLC circuit and how the components interact with the applied frequency to affect the RMS current. By analyzing the graph, students can visualize how the current changes with different frequencies and use given values to calculate key parameters such as the RMS voltage.
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