The e.m.f. induced in a secondary coil is `20000 V` when the current breaks in the primary coil. The mutual inductance is `5H` and the current reaches to zero in `10^(-4) sec` in the primary. The maximu current in the primary before it breaks is

Options

A. (a)`0.1 `A
B. (b)`0.4` A
C. (c)`0.6` A
D. (d)`0.8` A

Answer

To solve the problem step by step, we will use the formula for induced EMF in terms of mutual inductance and the rate of change of current.

### Step 1: Write down the formula for induced EMF
The induced EMF (E) in a coil due to a change in current in another coil is given by the formula:
\[ E = -M \frac{\Delta I}{\Delta t} \]
where:
- \(E\) is the induced EMF,
- \(M\) is the mutual inductance,
- \(\Delta I\) is the change in current,
- \(\Delta t\) is the time interval over which the change occurs.

### Step 2: Substitute the known values into the formula
From the problem, we know:
- \(E = 20000 \, V\)
- \(M = 5 \, H\)
- \(\Delta t = 10^{-4} \, s\)

Substituting these values into the formula, we have:
\[ 20000 = -5 \frac{\Delta I}{10^{-4}} \]

### Step 3: Rearrange the equation to solve for \(\Delta I\)
Rearranging the equation to isolate \(\Delta I\):
\[ \Delta I = -\frac{20000 \cdot 10^{-4}}{5} \]

### Step 4: Calculate \(\Delta I\)
Now, calculate \(\Delta I\):
\[ \Delta I = -\frac{20000 \cdot 10^{-4}}{5} = -\frac{20000}{5} \cdot 10^{-4} = -4000 \cdot 10^{-4} = -0.4 \, A \]

### Step 5: Determine the maximum current before it breaks
Since \(\Delta I\) represents the change in current, and it is negative, we can interpret this as the maximum current \(I\) in the primary coil before it breaks being:
\[ I = |\Delta I| = 0.4 \, A \]

### Conclusion
The maximum current in the primary before it breaks is \(0.4 \, A\).