The mutual inductance between a primary and secondary circuit is `0.5H`. The resistance of the primary and the secondary circuits are `20 ohms` and `5ohms` respectvely. To genrate a current of `0.4A` in the secondary,current in the primary must be changed at the rate of

Options

A. `4.0 As^(-1)`
B. `1.6As^(-1)`
C. `16.0As^(-1)`
D. `8.0As^(-1)`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the EMF in the Secondary Circuit
Using Ohm's Law, we know that the electromotive force (EMF) in the secondary circuit can be calculated as:

\[ E_2 = I_2 \times R_2 \]

Where:
- \( I_2 = 0.4 \, \text{A} \) (current in the secondary circuit)
- \( R_2 = 5 \, \Omega \) (resistance of the secondary circuit)

Substituting the values:

\[ E_2 = 0.4 \, \text{A} \times 5 \, \Omega = 2 \, \text{V} \]

### Step 2: Use the Mutual Inductance Formula
According to the concept of mutual inductance, the EMF in the secondary circuit is related to the rate of change of current in the primary circuit by the formula:

\[ E_2 = M \frac{di_1}{dt} \]

Where:
- \( M = 0.5 \, \text{H} \) (mutual inductance)
- \( \frac{di_1}{dt} \) is the rate of change of current in the primary circuit.

### Step 3: Rearrange the Formula to Find \( \frac{di_1}{dt} \)
We can rearrange the formula to solve for \( \frac{di_1}{dt} \):

\[ \frac{di_1}{dt} = \frac{E_2}{M} \]

### Step 4: Substitute the Values
Now, substituting the values we calculated:

\[ \frac{di_1}{dt} = \frac{2 \, \text{V}}{0.5 \, \text{H}} = 4 \, \text{A/s} \]

### Conclusion
Thus, the rate at which the current in the primary must be changed to generate a current of \( 0.4 \, \text{A} \) in the secondary is \( 4 \, \text{A/s} \).

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