An e.m.f of 5 millivolt is induced in a coil when in a nearby placed another coil the current changes by 5 ampere in 0.1 second . The coefficient of mutual induction between the two coils will be :

Options

A. 1 Henry
B. 0.1 Henry
C. 0.1 millihenry
D. 0.001 millihenry

Answer

To find the coefficient of mutual induction (M) between two coils, we can use the formula relating the induced electromotive force (e.m.f.) to the rate of change of current in the nearby coil. The formula is given by:

\[ \text{EMF} = M \frac{\Delta I}{\Delta t} \]

Where:
- EMF is the induced electromotive force (in volts),
- \( M \) is the mutual inductance (in henries),
- \( \Delta I \) is the change in current (in amperes),
- \( \Delta t \) is the change in time (in seconds).

### Step 1: Identify the given values
- Induced EMF, \( \text{EMF} = 5 \, \text{mV} = 5 \times 10^{-3} \, \text{V} \)
- Change in current, \( \Delta I = 5 \, \text{A} \)
- Change in time, \( \Delta t = 0.1 \, \text{s} \)

### Step 2: Rearrange the formula to solve for \( M \)
From the formula, we can rearrange it to find the mutual inductance \( M \):

\[ M = \frac{\text{EMF} \cdot \Delta t}{\Delta I} \]

### Step 3: Substitute the values into the equation
Now we can substitute the known values into the equation:

\[ M = \frac{(5 \times 10^{-3} \, \text{V}) \cdot (0.1 \, \text{s})}{5 \, \text{A}} \]

### Step 4: Calculate \( M \)
Calculating the numerator:

\[ 5 \times 10^{-3} \, \text{V} \times 0.1 \, \text{s} = 5 \times 10^{-4} \, \text{V.s} \]

Now substituting back into the equation for \( M \):

\[ M = \frac{5 \times 10^{-4} \, \text{V.s}}{5 \, \text{A}} = 1 \times 10^{-4} \, \text{H} \]

### Step 5: Convert to milliHenries
Since \( 1 \, \text{H} = 1000 \, \text{mH} \), we can convert:

\[ M = 1 \times 10^{-4} \, \text{H} = 0.1 \, \text{mH} \]

### Final Answer
The coefficient of mutual induction between the two coils is:

\[ M = 0.1 \, \text{mH} \]