An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 45.6 H inductor, determine the inductive reactance and the rms current through the inductor. HINT (a) the inductive reactance (in 0) (b) the rms current through the inductor (in A)

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**Title:** Determining Inductive Reactance and RMS Current in an AC Circuit

**Problem Statement:**

An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 45.6 H inductor, determine the inductive reactance and the rms current through the inductor.

**Hints and Steps to Solve:**

1. **Inductive Reactance (\(X_L\)) Calculation:**
   - Formula: \(X_L = 2\pi f L\)
   - Where:
     - \(f\) is the frequency (60.0 Hz)
     - \(L\) is the inductance (45.6 H)

   - **Input Field for Calculation:**
     - (a) The inductive reactance (in \(\Omega\)): 
       \[ \boxed{} \]

2. **RMS Current (\(I_{rms}\)) Calculation:**
   - Formula: \(I_{rms} = \frac{V_{rms}}{X_L}\)
   - Where:
     - \(V_{rms}\) is the rms voltage (120 V)

   - **Input Field for Calculation:**
     - (b) The rms current through the inductor (in A):
       \[ \boxed{} \, \text{A} \]

**Additional Resources:**

For further assistance, refer to the "Need Help?" section, where you can **Read It** for more detailed explanations.

**Note:**
- Ensure to use consistent units for calculations.
- Revisit the concepts of inductive reactance and rms current if needed.
Transcribed Image Text:**Title:** Determining Inductive Reactance and RMS Current in an AC Circuit **Problem Statement:** An AC power source has an rms voltage of 120 V and operates at a frequency of 60.0 Hz. If a purely inductive circuit is made from the power source and a 45.6 H inductor, determine the inductive reactance and the rms current through the inductor. **Hints and Steps to Solve:** 1. **Inductive Reactance (\(X_L\)) Calculation:** - Formula: \(X_L = 2\pi f L\) - Where: - \(f\) is the frequency (60.0 Hz) - \(L\) is the inductance (45.6 H) - **Input Field for Calculation:** - (a) The inductive reactance (in \(\Omega\)): \[ \boxed{} \] 2. **RMS Current (\(I_{rms}\)) Calculation:** - Formula: \(I_{rms} = \frac{V_{rms}}{X_L}\) - Where: - \(V_{rms}\) is the rms voltage (120 V) - **Input Field for Calculation:** - (b) The rms current through the inductor (in A): \[ \boxed{} \, \text{A} \] **Additional Resources:** For further assistance, refer to the "Need Help?" section, where you can **Read It** for more detailed explanations. **Note:** - Ensure to use consistent units for calculations. - Revisit the concepts of inductive reactance and rms current if needed.
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