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.