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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**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.
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: \( 0.207 \, \text{A} \) --- **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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