A `120` volt `AC` source is connected across a pure inductor of inductance `0.70` henry. If the frequency of the source is `60Hz`, the current passing through the inductor is

Options

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

Answer

To find the current passing through a pure inductor connected to an AC source, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Voltage (V) = 120 volts
- Inductance (L) = 0.70 henry
- Frequency (f) = 60 Hz

2. **Calculate the Inductive Reactance (X_L):**
The inductive reactance \( X_L \) can be calculated using the formula:
\[ X_L = 2 \pi f L \]
Substituting the values:
\[ X_L = 2 \pi (60) (0.70) \]

3. **Calculate \( X_L \):**
- First, calculate \( 2 \pi \):
\[ 2 \pi \approx 6.2832 \]
- Now, calculate \( X_L \):
\[ X_L = 6.2832 \times 60 \times 0.70 \]
- Performing the multiplication:
\[ X_L = 6.2832 \times 42 \approx 263.76 \, \text{ohms} \]

4. **Use Ohm's Law to Calculate Current (I):**
According to Ohm's Law, the current \( I \) can be calculated as:
\[ I = \frac{V}{X_L} \]
Substituting the values:
\[ I = \frac{120}{263.76} \]

5. **Calculate the Current (I):**
- Performing the division:
\[ I \approx 0.455 \, \text{amperes} \]

### Final Answer:
The current passing through the inductor is approximately **0.455 amperes**.

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