Remove the capacitor from the circuit in the figure and set R = 151 , L = 230 mH, fa = 60.0 Hz, and ɛm = 42.0 V. What are (a) Z, (b) p, and (c) I? ww ll (a) Number Units 2 174 (b) Number Units ° (degrees) -40.2 (c) Number Units 0.207 A
Remove the capacitor from the circuit in the figure and set R = 151 , L = 230 mH, fa = 60.0 Hz, and ɛm = 42.0 V. What are (a) Z, (b) p, and (c) I? ww ll (a) Number Units 2 174 (b) Number Units ° (degrees) -40.2 (c) Number Units 0.207 A
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Transcribed Image Text:**Problem Statement:**
Remove the capacitor from the circuit in the figure and set \( R = 151 \, \Omega \), \( L = 230 \, \text{mH} \), \( f_d = 60.0 \, \text{Hz} \), and \( \varepsilon_m = 42.0 \, \text{V} \). What are (a) \( Z \), (b) \( \phi \), and (c) \( I \)?
**Circuit Diagram:**
- The image shows a simple R-L series circuit.
- It consists of an AC voltage source (\( \varepsilon_g \)), a resistor (\( R \)), and an inductor (\( L \)).
- The capacitor (\( C \)) is labeled but needs to be removed as per instructions.
- The current (\( i \)) flows through the circuit.
**Given Values:**
- \( R = 151 \, \Omega \)
- \( L = 230 \, \text{mH} \)
- \( f_d = 60.0 \, \text{Hz} \)
- \( \varepsilon_m = 42.0 \, \text{V} \)
**Required:**
Determine the following:
(a) \( Z \) - Impedance
- Answer: \( 174 \, \Omega \)
(b) \( \phi \) - Phase angle
- Answer: \(-40.2 \, \text{degrees}\)
(c) \( I \) - Current
- Answer: \( 0.207 \, \text{A} \)
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**Calculation Notes:**
- To find the impedance \( Z \), use \( Z = \sqrt{R^2 + (X_L)^2} \), where \( X_L = 2\pi f_d L \).
- The phase angle \( \phi \) is calculated using \( \phi = \tan^{-1}\left(\frac{X_L}{R}\right) \).
- Current \( I \) is found using \( I = \frac{\varepsilon_m}{Z} \).
This exercise demonstrates the analysis of an R-L circuit without a capacitor, focusing on calculating impedance, phase angle, and current flow.
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