Question

In a series of L-R growth circuit, if maximum induced EMF in an inductor of inductance $3mH$ and $2A$ and $6V$ respectively, then time constant of the circuit is:
A) $1ms$
B) $\dfrac{1}{3}ms$
C) $\dfrac{1}{6}ms$
D) $\dfrac{1}{2}ms$

Answer 1

Hint- A LR circuit is a circuit having inductors and resistors. Inductors having Inductance L and the resistors of resistance R are connected in series. The time constant of the particular LR circuit is defined as the ratio of inductance and resistance connected in that circuit. And the time constant describes the growth or decay of current in the LR circuit. The time required for the LR circuit current to attain its maximum steady current.

Formula used:
$T = \dfrac{L}{R}$
Where
$T$=Time constant
L=Inductance
R=Resistance

Complete step by step answer:
(i) In the given LR circuit the inductor of inductance L and resistor of resistance R are connected in series. The LR circuit is connected across the voltage of 6V.
(ii) From the question we can understand that $L = 3mH$, ${I_{rms}} = 2A$ and $V = 6V$
(iii) To find the time constant T, we should know the value of resistance. Therefore by Ohm’s law, $V = {I_{rms}}R$
$\rightarrow R = \dfrac{V}{{{I_{rms}}}}$
$R = \dfrac{6}{2}$
$\therefore R = 3\Omega$
(iv)The time constant $T = \dfrac{L}{R}$
$\therefore T = \dfrac{{3mH}}{{3\Omega }}$
$T = 1ms$

Hence the correct option is A.

(v) The Time constant T has a unit as milli-seconds $(ms)$ as the inductance is measured in milli-henry $(mH)$

(vi)We know that the time required for the current in the LR circuit to attain its steady peak value is called the time constant $T$. The average time constant $T$ is equivalent to 5-time constants or 5T’s.

Note: The time constant in the LR circuit is used to describe the speed of the current attaining its maximum steady value. Hence the time constants are used to measure the speed of the LR circuits. The RMS current ${I_{rms}}$ means the root mean square value of current. It is the amount of current that dissipates the power in a resistor. The RMS value of the overall time of a periodic function is equivalent to the one period of that function.