In an electric circuit applied ac emf is `e=20 sin 300t` volt and the current is `i=4 sin 300t` ampere. The reactance of the circuit is-

Options

A. 5 ohm
B. 80 ohm
C. `1.8 k Omega`
D. zero

Answer

To find the reactance of the circuit given the applied AC emf and current, we can follow these steps:

### Step 1: Identify the given equations
The applied AC emf is given as:
\[ e = 20 \sin(300t) \, \text{volts} \]
The current in the circuit is given as:
\[ i = 4 \sin(300t) \, \text{amperes} \]

### Step 2: Compare with standard forms
The standard form for the AC voltage is:
\[ E = E_0 \sin(\omega t) \]
From the given equation, we can identify:
\[ E_0 = 20 \, \text{volts} \]

The standard form for the AC current is:
\[ I = I_0 \sin(\omega t) \]
From the given equation, we can identify:
\[ I_0 = 4 \, \text{amperes} \]

### Step 3: Calculate the reactance
The reactance \( X \) of the circuit can be calculated using the formula:
\[ X = \frac{E_0}{I_0} \]
Substituting the values we found:
\[ X = \frac{20}{4} = 5 \, \text{ohms} \]

### Conclusion
The reactance of the circuit is:
\[ X = 5 \, \text{ohms} \]