If a current of 3A flowing in the primary coil is reduced to zero in 0.01 s then the induced emf in the secondary coil is 1500 V, the mutual inductance between the two coils is :

Options

A. 0.5 H
B. 1.5 H
C. 5 H
D. 10 H

Answer

To find the mutual inductance between the two coils, we can use the formula relating induced electromotive force (emf), mutual inductance, and the rate of change of current in the primary coil.

### Given:
- Current in primary coil (I) = 3 A
- Current is reduced to 0 A in time (Δt) = 0.01 s
- Induced emf in secondary coil (E) = 1500 V

### Step 1: Calculate the rate of change of current (dI/dt)
The rate of change of current can be calculated using the formula:
\[ \frac{dI}{dt} = \frac{I_f - I_i}{\Delta t} \]
Where:
- \(I_f\) = final current = 0 A
- \(I_i\) = initial current = 3 A

Substituting the values:
\[ \frac{dI}{dt} = \frac{0 - 3}{0.01} = \frac{-3}{0.01} = -300 \, \text{A/s} \]

### Step 2: Use the formula for induced emf
The induced emf in the secondary coil is given by:
\[ E = -M \frac{dI}{dt} \]
Where:
- \(E\) = induced emf
- \(M\) = mutual inductance
- \(\frac{dI}{dt}\) = rate of change of current

### Step 3: Rearranging the formula to find mutual inductance (M)
Rearranging the equation to solve for \(M\):
\[ M = -\frac{E}{\frac{dI}{dt}} \]

### Step 4: Substitute the values into the equation
Substituting the values we have:
\[ M = -\frac{1500}{-300} = \frac{1500}{300} = 5 \, \text{H} \]

### Final Answer:
The mutual inductance between the two coils is \(5 \, \text{H}\).

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