Question

A current of 2 A is passed through the primary coil. The total flux linked with the secondary coil, which is closely wound over the primary is \( 2000 \times 10^{-6} \, \text{weber} \). What is the induced emf in the secondary if the current through the primary increases at a rate of \( 0.2 \, \text{A s}^{-1} \)?

• A. \( 2 \times 10^{-4} \, V \)
• B. \( 4 \times 10^{-4} \, V \)
• C. \( 1 \times 10^{-4} \, V \)
• D. \( 8 \times 10^{-4} \, V \)

Hint:

Mutual inductance relates flux in one coil to current in another. Always compute \( M \) first if flux and current are given.

Answer 1

The Correct Option is A

Step 1: Use definition of mutual inductance.
\[ M = \frac{\Phi}{I} \]

Step 2: Substitute given values.
\[ \Phi = 2000 \times 10^{-6} = 2 \times 10^{-3} \, Wb \]
\[ I = 2A \]

Step 3: Calculate mutual inductance.
\[ M = \frac{2 \times 10^{-3}}{2} = 1 \times 10^{-3} \, H \]

Step 4: Use induced emf formula.
\[ \mathcal{E} = M \frac{dI}{dt} \]

Step 5: Substitute rate of current change.
\[ \frac{dI}{dt} = 0.2 \, A/s \]

Step 6: Calculate emf.
\[ \mathcal{E} = (1 \times 10^{-3})(0.2) \]
\[ \mathcal{E} = 2 \times 10^{-4} \, V \]

Step 7: Final Answer.
\[ \boxed{2 \times 10^{-4} \, V} \]