The value of the current through an inductance of `1H` and of negligible resistance, when connected through an AC source of `200V` and `50Hz` is

Options

A. `0.637A`
B. `1.637A`
C. `2.637 A`
D. `3.637A`

Explanation

To find the current through an inductance of 1 H when connected to an AC source of 200 V and 50 Hz, we will follow these steps:

### Step 1: Understand the relationship between voltage, current, and impedance in an AC circuit.
In an AC circuit, the current (I) can be calculated using the formula:
\[ I = \frac{V}{Z} \]
where \( V \) is the voltage and \( Z \) is the impedance.

### Step 2: Determine the impedance in the circuit.
Since the resistance is negligible, the impedance \( Z \) in this case will be purely inductive, which means:
\[ Z = X_L \]
where \( X_L \) is the inductive reactance.

### Step 3: Calculate the inductive reactance.
The inductive reactance \( X_L \) is given by the formula:
\[ X_L = \omega L \]
where \( \omega \) (angular frequency) is given by:
\[ \omega = 2 \pi f \]
and \( f \) is the frequency in hertz.

### Step 4: Substitute the values.
Given:
- \( L = 1 \, \text{H} \)
- \( f = 50 \, \text{Hz} \)

Calculate \( \omega \):
\[ \omega = 2 \pi (50) = 100\pi \, \text{rad/s} \]

Now, calculate \( X_L \):
\[ X_L = \omega L = (100\pi)(1) = 100\pi \, \Omega \]

### Step 5: Calculate the current.
Now substitute \( V = 200 \, \text{V} \) and \( X_L = 100\pi \, \Omega \) into the current formula:
\[ I = \frac{V}{X_L} = \frac{200}{100\pi} = \frac{2}{\pi} \, \text{A} \]

### Step 6: Calculate the numerical value.
Using \( \pi \approx 3.14 \):
\[ I \approx \frac{2}{3.14} \approx 0.637 \, \text{A} \]

### Final Answer:
The value of the current through the inductance is approximately \( 0.637 \, \text{A} \).

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