Solveeit Logo

Question

Question: In the figure shown, a circuit contains two identical resistors with resistance \(R = 5\Omega \) and...

In the figure shown, a circuit contains two identical resistors with resistance R=5ΩR = 5\Omega and an inductance with L=2mHL = 2mH. An ideal battery of 15V15V is connected in the circuit. What will be the current through the battery long after the switch is closed?

(A) 6A6A
(B) 7.5A7.5A
(C) 5.5A5.5A
(D) 3A3A

Explanation

Solution

You must know the behaviour of the inductors, resistors and the capacitors after the switch is closed. You must also know that the value of the current and charge depends upon the time they pass in the circuit. Also remember that the inductor will behave as a zero resistance wire after passing a long time in a circuit.

Formula used:
i=VRi = \dfrac{V}{R}
Where ii is the current flowing
VV is the voltage difference
RR is the resistance

Complete step by step answer:
As we know that the the inductor behaves as a plane wire or a zero resistance wire after it passes a long time in a circuit, for tt \to \infty
So, after circuit will become like,

Here, the switch is closed for a long time so the inductor behaves as a zero resistance wire, so we remove the inductor and place a plane wire over there.
Now, we have only two resistance of same value which are connected as parallel to each other, so the Req{R_{eq}} for this is given by,
Req=R2{R_{eq}} = \dfrac{R}{2}
And the voltage of the battery connected is given as,
V=15VV = 15V
By applying the formula for the current,
i=VReqi = \dfrac{V}{{{R_{eq}}}}
Where ii is the current flowing in the circuit
VV is the voltage difference across the circuit
Req{R_{eq}} is the equivalent resistance of the circuit
On putting all the values of the variable we have,
i=15×2R\Rightarrow i = \dfrac{{15 \times 2}}{R} {\therefore Req=R2{R_{eq}} = \dfrac{R}{2} }
We have also given the value of RRin the question that is,
R=5ΩR = 5\Omega
On putting that in the above equation, we get
i=15×25\Rightarrow i = \dfrac{{15 \times 2}}{5}
On further solving, we get the value of current through the battery long after the switch is closed is,
i=6Ai = 6A

Therefore, the correct option is option (A).

Note: The effect of an inductor in a circuit is to oppose changes in current through it by developing a voltage across it proportional to the rate of change of the current. Inductors are used to create magnetic fields in electrical machines for the purpose of energy conversion. For DC current, inductors act as a simple wire but for AC, they oppose the current change in circuits.