The coefficient of mutual inductance between the primary and secondary of the coil is 5H .A current of 10 A is cut - off in 0.5 s . The induced emf is :

Options

A. 1 V
B. 10 V
C. 5 V
D. 100 V

Answer

To solve the problem, we will use the formula for induced electromotive force (emf) due to mutual inductance. The formula is given by:

\[ E = -M \frac{dI}{dt} \]

Where:
- \(E\) is the induced emf,
- \(M\) is the coefficient of mutual inductance,
- \(\frac{dI}{dt}\) is the rate of change of current.

### Step 1: Identify the given values
From the problem, we have:
- Coefficient of mutual inductance, \(M = 5 \, \text{H}\)
- Initial current, \(I_1 = 10 \, \text{A}\)
- Final current, \(I_2 = 0 \, \text{A}\)
- Time interval, \(\Delta t = 0.5 \, \text{s}\)

### Step 2: Calculate the change in current (\(\Delta I\))
The change in current can be calculated as:
\[ \Delta I = I_2 - I_1 = 0 \, \text{A} - 10 \, \text{A} = -10 \, \text{A} \]

### Step 3: Calculate the rate of change of current (\(\frac{dI}{dt}\))
The rate of change of current is given by:
\[ \frac{dI}{dt} = \frac{\Delta I}{\Delta t} = \frac{-10 \, \text{A}}{0.5 \, \text{s}} = -20 \, \text{A/s} \]

### Step 4: Substitute the values into the induced emf formula
Now we can substitute the values into the induced emf formula:
\[ E = -M \frac{dI}{dt} = -5 \, \text{H} \times (-20 \, \text{A/s}) \]

### Step 5: Calculate the induced emf
Calculating the above expression gives:
\[ E = 5 \times 20 = 100 \, \text{V} \]

### Final Answer
The induced emf is \(100 \, \text{V}\).

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