Question

In a $LR$ circuit, \[R = 10\Omega \] and \[L = 2H\]. If an alternating voltage of $120V$ and $60Hz$ is connected in this circuit, then the value current flowing in it will be ____________$A$(nearly)
A) \[0.32\]
B) $0.16$
C) $0.48$
D) $0.8$

Answer 1

Hint-A $LR$ circuit is a circuit having inductors and resistors having Inductance $L$ and the resistors of resistance $R$ are connected in series. The LR series connected across the voltage is called the $LR$ series circuit. The effective resistance in the circuit having both resistance and inductance is called impedance. The impedance gives resistance to the flowing AC current in the $LR$ circuit.

Formula used:
(i) \[V = IR\]
(ii) \[Z = \sqrt {{R^2} + X_L^2} \]
Where,
$V$= potential
$I$= current
$R$= resistance
\[Z\]=impedance
\[{X_L}\]=Inductance

Complete step by step answer:
(i) We can find the value of current flowing in the circuit using Ohm’s law \[V = IR\]. Here we have the value of potential difference 120V. In LR circuits, resistance is in the form of impedance. Therefore impedance, \[Z = \sqrt {{R^2} + X_L^2} \]
\[Z = \sqrt {{R^2} + {{(2\pi fL)}^2}} \]
(ii) Applying the given values in the above formula,
\[Z = \sqrt {{{(10)}^2} + {{(2 \times 3.14 \times 60 \times 2)}^2}} \]
\[Z = \sqrt {100 + 567912.96} \]
\[ \rightarrow Z = \sqrt {568012.96} \]
\[\therefore Z = 753.66\]
(iii) In Ohm’s law\[V = IR\]. The current flowing in the circuit is\[ \Rightarrow I = \dfrac{V}{R}\]. For LR circuit, the current flowing in the circuit is \[I = \dfrac{V}{Z}\]
\[ \rightarrow I = \dfrac{{120}}{{753.66}}\]
\[\therefore I = 0.159A\]
Hence \[I = 0.16A\](approximately)

therefore the correct option is B.

Additional information:
(i) The LR series circuit is used in circuits called tank circuits, resonant circuits and tuning circuits.
(ii) 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.

Note: 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. RMS value of current and voltage are very important. Because the AC voltage current and voltages keep on changing. If we want to build an equivalent AC circuit for the particular DC circuit means we can use the RMS value of current and voltage.