Question

Mutual inductance between two coils is \(2\,H\). Current changes from \(0\) to \(10\,A\) in \(0.5\,s\). Find the induced emf.

• A. \(20\,V\)
• B. \(60\,V\)
• C. \(40\,V\)
• D. \(80\,V\)

Hint:

For mutual induction problems, induced emf equals mutual inductance multiplied by the rate of change of current.

Answer 1

The Correct Option is C

Concept: According to the principle of mutual induction, the induced emf is \[ e=M\frac{dI}{dt} \] where \(M\) is the mutual inductance.

Step 1: Write the given values. \[ M=2\,H \] \[ \Delta I=10-0=10\,A \] \[ \Delta t=0.5\,s \]

Step 2: Calculate rate of change of current. \[ \frac{\Delta I}{\Delta t} = \frac{10}{0.5} = 20\,A\,s^{-1} \]

Step 3: Apply mutual induction formula. \[ e=M\frac{\Delta I}{\Delta t} \] \[ =2\times20 \] \[ =40\,V \]

Step 4: Final answer. \[ \boxed{40\,V} \] Hence, \[ \boxed{(C)} \]