A coil of inductor'L' is connected to an a.c. source of emf E and frequency 'f'. The current in the coil is

Options

A. `(E)/(sqrt2pifL)`
B. `(E)/(2pifL)`
C. `(E^2)/(2pifL)`
D. `(E)/(2pifL^2)`

Answer

To find the current in a coil of inductance \( L \) connected to an AC source of EMF \( E \) and frequency \( f \), we can follow these steps:

### Step 1: Understand the Concept of Inductive Reactance
Inductive reactance (\( X_L \)) is the opposition that an inductor offers to the flow of alternating current (AC). It is given by the formula:
\[ X_L = \omega L \]
where \( \omega \) is the angular frequency.

### Step 2: Relate Angular Frequency to Frequency
The angular frequency (\( \omega \)) is related to the frequency (\( f \)) by the equation:
\[ \omega = 2\pi f \]

### Step 3: Substitute Angular Frequency into Inductive Reactance
Substituting the expression for \( \omega \) into the formula for inductive reactance, we get:
\[ X_L = 2\pi f L \]

### Step 4: Apply Ohm's Law
According to Ohm's Law, the current (\( I \)) flowing through the circuit can be expressed as:
\[ I = \frac{V}{R} \]
In this case, the voltage \( V \) is the EMF \( E \), and the resistance \( R \) is the inductive reactance \( X_L \). Therefore, we can write:
\[ I = \frac{E}{X_L} \]

### Step 5: Substitute Inductive Reactance into the Current Formula
Now, substituting \( X_L \) into the equation for current, we have:
\[ I = \frac{E}{2\pi f L} \]

### Conclusion
Thus, the current in the coil is given by:
\[ I = \frac{E}{2\pi f L} \]

### Final Answer
The correct option for the current in the coil is:
\[ \text{Option 2: } \frac{E}{2\pi f L} \]