The inductive reactance of a coil of 0.2 H inductance at a frequecy of 60 Hz is

Options

A. `7.54 Omega`
B. `0.754 Omega`
C. `75.4 Omega`
D. `7.54 xx 10^(-3) Omega`

Answer

To find the inductive reactance (XL) of a coil with an inductance (L) of 0.2 H at a frequency (f) of 60 Hz, we can use the formula for inductive reactance:

### Step-by-Step Solution:

1. **Understand the formula for inductive reactance:**
The inductive reactance (XL) is given by the formula:
\[ XL = \omega \cdot L \]
where \(\omega\) (angular frequency) is calculated as:
\[ \omega = 2\pi f \]

2. **Substitute the frequency into the angular frequency formula:**
Given that the frequency \(f = 60 \, \text{Hz}\):
\[ \omega = 2 \pi (60) \]

3. **Calculate \(\omega\):**
Using the value of \(\pi \approx 3.14\):
\[ \omega = 2 \cdot 3.14 \cdot 60 = 376.8 \, \text{rad/s} \]

4. **Substitute \(\omega\) and \(L\) into the inductive reactance formula:**
Now, substituting \(\omega\) and \(L\) into the formula for XL:
\[ XL = 376.8 \cdot 0.2 \]

5. **Calculate XL:**
\[ XL = 75.36 \, \Omega \]

6. **Round the answer:**
The inductive reactance can be rounded to:
\[ XL \approx 75.4 \, \Omega \]

### Final Answer:
The inductive reactance of the coil at a frequency of 60 Hz is approximately **75.4 Ω**.