Question 156: Electromagnetic Induction

Question

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of $8 \mathrm{~A} / \mathrm{s}$. At an instant when R is $12 \Omega$, the value of the current in the circuit will be ________ A.

Accepted Answer

To analyze the given circuit, we can use the equation for induced electromotive force (EMF) in an inductor. The formula is:
$ \varepsilon - \frac{L \, dI}{dt} - I \cdot R = 0 $
For this circuit, we have:
$ \varepsilon = 12 \, 	ext{V} $ (the applied EMF)
$ L = 3 \, 	ext{H} $ (the inductance of the inductor)
$ \frac{dI}{dt} = 8 \, 	ext{A/s} $ (the rate of change of current)
Assuming the direction of current is such that the change in current is negative, substitute these values into the equation:
$ 12 - 3 	imes (-8) - I 	imes 12 = 0 $
Solving for $ I $ (the current in the circuit):
$ 12 + 24 - 12I = 0 $
$ 36 = 12I $
$ I = \frac{36}{12} = 3 \, 	ext{A} $
Thus, the current at the moment when the resistance $ R $ is $ 12 \, \Omega $ is $ 3 \, 	ext{A} $.

Electromagnetic Induction

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 \mathrm{~A} / \mathrm{s}. At an instant when R is 12 \Omega, the value of the current in the circuit will be ________ A.

Choose the correct answer: