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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![**Question:**
What is the RMS current in amps in a series circuit with a resistor \( R = 95.0 \, \Omega \), a capacitor \( C = 0.338 \, \mu F \), and an AC source that provides an RMS voltage of 25.4 volts at 4.92 kHz? (State answer with three digits right of decimal. Do not include unit.)
**Response Field:**
[Blank space for response]
---
**Notes for Educators:**
This question involves calculating the RMS current in a series RC circuit. The formula to find the total impedance \( Z \) in a series resistor-capacitor circuit is:
\[ Z = \sqrt{R^2 + (X_C)^2} \]
Where the capacitive reactance \( X_C \) is given by:
\[ X_C = \frac{1}{2 \pi f C} \]
With:
- \( R = 95.0 \, \Omega \)
- \( C = 0.338 \times 10^{-6} \, F \)
- \( f = 4.92 \times 10^3 \, Hz \)
To find the RMS current (\( I_{RMS} \)), use Ohm's Law for AC circuits:
\[ I_{RMS} = \frac{V_{RMS}}{Z} \]
Where \( V_{RMS} = 25.4 \, V \).
Ensure the student calculates \( X_C \) first, then uses it to find \( Z \), and finally calculates \( I_{RMS} \). Encourage showing each calculation step clearly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bd4008c-0e04-4739-a817-034fe415e209%2F7bc5e064-615f-4b27-b567-93910e1026dd%2Fh9pv80n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the RMS current in amps in a series circuit with a resistor \( R = 95.0 \, \Omega \), a capacitor \( C = 0.338 \, \mu F \), and an AC source that provides an RMS voltage of 25.4 volts at 4.92 kHz? (State answer with three digits right of decimal. Do not include unit.)
**Response Field:**
[Blank space for response]
---
**Notes for Educators:**
This question involves calculating the RMS current in a series RC circuit. The formula to find the total impedance \( Z \) in a series resistor-capacitor circuit is:
\[ Z = \sqrt{R^2 + (X_C)^2} \]
Where the capacitive reactance \( X_C \) is given by:
\[ X_C = \frac{1}{2 \pi f C} \]
With:
- \( R = 95.0 \, \Omega \)
- \( C = 0.338 \times 10^{-6} \, F \)
- \( f = 4.92 \times 10^3 \, Hz \)
To find the RMS current (\( I_{RMS} \)), use Ohm's Law for AC circuits:
\[ I_{RMS} = \frac{V_{RMS}}{Z} \]
Where \( V_{RMS} = 25.4 \, V \).
Ensure the student calculates \( X_C \) first, then uses it to find \( Z \), and finally calculates \( I_{RMS} \). Encourage showing each calculation step clearly.
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