Question

Consider a series L-R circuit in which $ L = \dfrac{1}{\pi }H $ and resistance $ R = 100\Omega $ . When the circuit is connected to A.C. source $ 220V $ , $ 50Hz $ . Find the current drawn from the source.

Answer 1

Hint: Find the current using ohm’s law which gives the relation between current, voltage, and resistance. But we have been given an L-R circuit so resistance in the L-R circuit is equal to impedance. Use the formula of impedance and find the value of impedance. Use that value and value of voltage to find the desired current.

Complete Step By Step Answer:
In an L-R circuit the resistance offered by the circuit is known as impedance denoted by $ Z $
For finding the impedance,
 $ Z = \sqrt {{R^2} + {X_L}^2} $
Where, $ R $ is the resistance and $ {X_L} $ is the inductive reactance. Inductive reactance is the effect of reducing the current flow of an alternating or changing current in an inductor.
We know, $ {X_L} = \omega L $
Where, $ \omega $ is the frequency and can also be written as, $ \omega = 2\pi f $
 $ \Rightarrow {X_L} = 2\pi fL $
Putting this in the above equation
 $ \Rightarrow Z = \sqrt {{R^2} + {{(2\pi fL)}^2}} $
We have been given, $ L = \dfrac{1}{\pi }H $ and resistance $ R = 100\Omega $ and frequency $ f = 50Hz $
 $ \Rightarrow Z = \sqrt {{{100}^2} + 2\pi \times 50 \times \dfrac{1}{\pi }} $
 $ \Rightarrow Z = 100\sqrt 2 \Omega $
We have been given voltage $ {V_{rms}} = 220V $
Using these values to find current
we will find the current in the circuit using ohm’s law.
 $ {I_{rms}} = \dfrac{{{V_{rms}}}}{Z} $
 $ \Rightarrow {I_{rms}} = \dfrac{{220}}{{100\sqrt 2 }} $
 $ \Rightarrow {I_{rms}} = 1.1\sqrt 2 A $
Hence the current drawn from the source is $ 1.1\sqrt 2 A $ .

Note:
Ohm’s law states that the current in the circuit is directly proportional to the voltage across the circuit and inversely proportional to the resistance offered by that circuit. Because of its inductance, an inductor inhibits the flow of an alternating current. As a result of Lenz's Law, any inductor opposes a change in current. The inductive reactance of an inductor determines how much it obstructs current flow.