A `0.7` henry inductor is connected across a `120 V-60 Hz AC` source. The current in the inductor will be very nearly

Options

A. `4.55`amp
B. `0.355`amp
C. `0.455`amp
D. `3.55`amp

Answer

To solve the problem, we need to calculate the current flowing through a 0.7 Henry inductor when connected to a 120 V, 60 Hz AC source. We will follow these steps:

### Step 1: Calculate the Inductive Reactance (XL)
The inductive reactance (XL) is given by the formula:
\[ X_L = \omega L \]
where \(\omega = 2\pi f\) and \(f\) is the frequency in hertz.

Given:
- \(L = 0.7 \, \text{H}\)
- \(f = 60 \, \text{Hz}\)

First, we calculate \(\omega\):
\[ \omega = 2\pi \times 60 \approx 376.99 \, \text{rad/s} \]

Now, we can calculate \(X_L\):
\[ X_L = \omega L = 376.99 \times 0.7 \approx 263.89 \, \Omega \]

### Step 2: Calculate the RMS Current (I)
The RMS current can be calculated using Ohm's law for AC circuits:
\[ I_{rms} = \frac{V_{rms}}{X_L} \]

Given:
- \(V_{rms} = 120 \, \text{V}\)

Now, substituting the values:
\[ I_{rms} = \frac{120}{263.89} \approx 0.455 \, \text{A} \]

### Conclusion
The current in the inductor will be very nearly \(0.455 \, \text{A}\).