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The graph below represents the voltage and current of a series RLC circuit. a) Find R b) Find the resonance frequency if L = 200 µH

The graph below represents the voltage and current of a series RLC circuit. a) Find R b) Find the resonance frequency if L = 200 µH

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The graph below represents the voltage and current of a series RLC circuit.
a) Find R
b) Find the resonance frequency if L = 200 µH 

**Understanding Voltage and Current Waveforms** The provided image displays a graph with two sinusoidal waveforms, representing voltage (denoted as \( E \)) and current (denoted as \( i \)) over time. ### Graph and Axes Explanation: - **Horizontal Axis (Time Axis):** - Denoted in microseconds (µs), the time axis spans from 0 to 100 µs, marked at intervals of 50 µs. - **Vertical Axes:** - **Left Vertical Axis (Voltage):** - Denoted in volts (V), it ranges from -10 V to 10 V. - **Right Vertical Axis (Current):** - Denoted in amperes (A), it ranges from -2 A to 2 A. ### Voltage and Current Waveforms: - **Voltage Waveform (Purple Curve):** - The voltage waveform is a sinusoidal curve originating at 0 V at \( t = 0 \) µs. - It peaks at 10 V at approximately 25 µs and -10 V at around 75 µs, then returns to 0 V at 100 µs. - **Current Waveform (Green Curve):** - The current waveform, similarly sinusoidal, also starts at 0 A at \( t = 0 \) µs. - It peaks at 2 A at around 50 µs and -2 A at about 100 µs, similarly returning to 0 A at 100 µs. ### Observations: - **Phase Difference:** - It can be observed that there is a phase difference between the voltage and current waveforms. The voltage peaks and zero crossings are not aligned exactly with those of the current. The current appears to lag behind the voltage. ### Educational Value: Such graphs are critical in understanding AC (alternating current) circuits where voltage and current vary sinusoidally over time. The phase difference between the voltage and current is crucial in analyzing the power factor and energy flow in the circuit. **Conclusion:** The graph helps visualize the relationship between current and voltage in AC circuits, highlighting the phase difference and how the sinusoidal variations interact over time.
Transcribed Image Text:**Understanding Voltage and Current Waveforms** The provided image displays a graph with two sinusoidal waveforms, representing voltage (denoted as \( E \)) and current (denoted as \( i \)) over time. ### Graph and Axes Explanation: - **Horizontal Axis (Time Axis):** - Denoted in microseconds (µs), the time axis spans from 0 to 100 µs, marked at intervals of 50 µs. - **Vertical Axes:** - **Left Vertical Axis (Voltage):** - Denoted in volts (V), it ranges from -10 V to 10 V. - **Right Vertical Axis (Current):** - Denoted in amperes (A), it ranges from -2 A to 2 A. ### Voltage and Current Waveforms: - **Voltage Waveform (Purple Curve):** - The voltage waveform is a sinusoidal curve originating at 0 V at \( t = 0 \) µs. - It peaks at 10 V at approximately 25 µs and -10 V at around 75 µs, then returns to 0 V at 100 µs. - **Current Waveform (Green Curve):** - The current waveform, similarly sinusoidal, also starts at 0 A at \( t = 0 \) µs. - It peaks at 2 A at around 50 µs and -2 A at about 100 µs, similarly returning to 0 A at 100 µs. ### Observations: - **Phase Difference:** - It can be observed that there is a phase difference between the voltage and current waveforms. The voltage peaks and zero crossings are not aligned exactly with those of the current. The current appears to lag behind the voltage. ### Educational Value: Such graphs are critical in understanding AC (alternating current) circuits where voltage and current vary sinusoidally over time. The phase difference between the voltage and current is crucial in analyzing the power factor and energy flow in the circuit. **Conclusion:** The graph helps visualize the relationship between current and voltage in AC circuits, highlighting the phase difference and how the sinusoidal variations interact over time.
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