Question

When a current passing through a coil changes at a rate of 30 A s\(^{-1}\), the emf induced in the coil is 12 V. If the current passing through this coil changes at a rate of 20 A s\(^{-1}\), the emf induced in this coil is:

• A. 8 V
• B. 10 V
• C. 2.5 V
• D. 3 V
• E. 5 V

Hint:

Remember that the induced emf is directly proportional to the rate of change of current. If the rate of change decreases, the induced emf will also decrease proportionally.

Answer 1

The Correct Option is A

The induced emf in a coil is related to the rate of change of current through the coil, according to Faraday's law of electromagnetic induction: \[ \mathcal{E} = -L \frac{dI}{dt} \] Where: - \( \mathcal{E} \) is the induced emf,
- \( L \) is the inductance of the coil,
- \( \frac{dI}{dt} \) is the rate of change of current.
From the first scenario: \[ \mathcal{E}_1 = 12 \, {V}, \quad \frac{dI_1}{dt} = 30 \, {A/s} \] Using the formula: \[ 12 = -L \times 30 \quad \Rightarrow \quad L = \frac{12}{30} = 0.4 \, {H} \] Now, for the second scenario: \[ \frac{dI_2}{dt} = 20 \, {A/s} \] Using the same formula for the emf: \[ \mathcal{E}_2 = -L \times \frac{dI_2}{dt} = -0.4 \times 20 = 8 \, {V} \] Thus, the induced emf is 8 V.