Your team has used a data logger with graphing software to take data on the voltage across the capacitor in the series RLC circuit in the figures below. **Figure Descriptions:** - **Figure a:** Contains a series RLC circuit with a switch set to position \( a \), indicating that the capacitor is charged. The circuit includes a voltage source \(\mathcal{E}\), an inductor \( L \), a resistor \( R \), and a capacitor \( C \). The capacitor is charged in this position. - **Figure b:** Shows the same RLC circuit, but the switch is moved to position \( b \), initiating oscillations in the circuit. Switch \( S \) has been at position \( a \) for a very long time and is then thrown to position \( b \). The capacitance \( C \) is known to be \( 20.0 \, \mu \text{F} \). The data logger creates a graph of the voltage across the capacitor as a function of time, with \( t = 0 \) being the instant the switch is moved to position \( b \). The graph is provided below. **Graph Explanation:** - The vertical axis represents the voltage change \(\Delta V\) in volts (V), ranging from -30 V to 30 V. - The horizontal axis represents time \( t \) in milliseconds (ms), ranging from 0 ms to 50 ms. - The graph illustrates oscillations starting at around 30 V, decreasing over time in amplitude, reflecting the damped oscillatory nature of the RLC circuit. **Activity:** Using the graph, discuss this situation in your group and determine: (a) The emf of the battery (\(\mathcal{E}\)) is 30 V. (b) The inductance (\(L\)) in Henries (H). (c) The resistance (\(R\)) in Ohms (\(\Omega\)). For tasks (b) and (c), the values determined are currently incorrect, indicated by a cross (\(\times\)).
Your team has used a data logger with graphing software to take data on the voltage across the capacitor in the series RLC circuit in the figures below. **Figure Descriptions:** - **Figure a:** Contains a series RLC circuit with a switch set to position \( a \), indicating that the capacitor is charged. The circuit includes a voltage source \(\mathcal{E}\), an inductor \( L \), a resistor \( R \), and a capacitor \( C \). The capacitor is charged in this position. - **Figure b:** Shows the same RLC circuit, but the switch is moved to position \( b \), initiating oscillations in the circuit. Switch \( S \) has been at position \( a \) for a very long time and is then thrown to position \( b \). The capacitance \( C \) is known to be \( 20.0 \, \mu \text{F} \). The data logger creates a graph of the voltage across the capacitor as a function of time, with \( t = 0 \) being the instant the switch is moved to position \( b \). The graph is provided below. **Graph Explanation:** - The vertical axis represents the voltage change \(\Delta V\) in volts (V), ranging from -30 V to 30 V. - The horizontal axis represents time \( t \) in milliseconds (ms), ranging from 0 ms to 50 ms. - The graph illustrates oscillations starting at around 30 V, decreasing over time in amplitude, reflecting the damped oscillatory nature of the RLC circuit. **Activity:** Using the graph, discuss this situation in your group and determine: (a) The emf of the battery (\(\mathcal{E}\)) is 30 V. (b) The inductance (\(L\)) in Henries (H). (c) The resistance (\(R\)) in Ohms (\(\Omega\)). For tasks (b) and (c), the values determined are currently incorrect, indicated by a cross (\(\times\)).
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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Transcribed Image Text:Your team has used a data logger with graphing software to take data on the voltage across the capacitor in the series RLC circuit in the figures below.
**Figure Descriptions:**
- **Figure a:** Contains a series RLC circuit with a switch set to position \( a \), indicating that the capacitor is charged. The circuit includes a voltage source \(\mathcal{E}\), an inductor \( L \), a resistor \( R \), and a capacitor \( C \). The capacitor is charged in this position.
- **Figure b:** Shows the same RLC circuit, but the switch is moved to position \( b \), initiating oscillations in the circuit.
Switch \( S \) has been at position \( a \) for a very long time and is then thrown to position \( b \). The capacitance \( C \) is known to be \( 20.0 \, \mu \text{F} \). The data logger creates a graph of the voltage across the capacitor as a function of time, with \( t = 0 \) being the instant the switch is moved to position \( b \). The graph is provided below.
**Graph Explanation:**
- The vertical axis represents the voltage change \(\Delta V\) in volts (V), ranging from -30 V to 30 V.
- The horizontal axis represents time \( t \) in milliseconds (ms), ranging from 0 ms to 50 ms.
- The graph illustrates oscillations starting at around 30 V, decreasing over time in amplitude, reflecting the damped oscillatory nature of the RLC circuit.
**Activity:**
Using the graph, discuss this situation in your group and determine:
(a) The emf of the battery (\(\mathcal{E}\)) is 30 V.
(b) The inductance (\(L\)) in Henries (H).
(c) The resistance (\(R\)) in Ohms (\(\Omega\)).
For tasks (b) and (c), the values determined are currently incorrect, indicated by a cross (\(\times\)).
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