Question

The current following through an inductance coil of self inductance 6 mH at different time instants is as shown. The emf induced between t = 20s and t = 40s is nearly

• A. 2 × 10^-2 V
• B. 3 × 10^-4 V
• C. 4 × 10^-3 V
• D. 30 × 10² V

Answer 1

The Correct Option is B

The equations describe the induced electromotive force (emf) in a circuit:

\[ |e| = L \frac{dI}{dt} \]

The magnitude of the emf (\(|e|\)) is given by the product of inductance (\(L\)) and the rate of change of current (\(\frac{dI}{dt}\)).

\[ |e| = 6 \times 10^{-3} \left[ \frac{I_2 - I_1}{t_2 - t_1} \right] \]

Substituting the values, the emf is calculated using the discrete current change over time.

\[ |e| = 6 \times 10^{-3} \left[ \frac{1}{40 - 20} \right] \]

Plugging in the specific time interval (\(t_1 = 20\), \(t_2 = 40\)) and assuming the current change (\(\Delta I = 1\)).

\[ e = 3 \times 10^{-4} \text{ V} \]

The final result for the induced emf is \(3 \times 10^{-4}\) volts.