# An inductor and resistor are connected in series with an AC source. In this circuit,

The current and the PD across resistance lead the PD across the inductance.

(A) The current and the PD across the resistance lag behind the PD across the inductance by angle $\dfrac{\pi }{2}$

(B) The current and the PD across the resistance lag behind the PD across the inductance by an angle $\pi $

(C) The PD across the resistance lags behind the PD across the inductance by an angle (D)$\dfrac{\pi }{2}$ but the current in resistance leads the PD across the inductance by $\dfrac{\pi }{2}$.

Answer

Verified

290.4k+ views

**Hint**Find the impedance for series resistance and inductor AC circuit then, draw the phasor diagram of series inductance and resistance series AC circuit. In the phasor diagram, draw the voltage across resistance and also draw the voltage across inductance. If the angle of voltage across inductance is greater then it leads the voltage across resistance.

**Step by Step Solution**

Let the resistance and inductance be R and L respectively

Construct a series L-R AC circuit

Now, we get

${V_{net}} = {\vec V_L} + {\vec V_R}$

By taking magnitude

\[

\left| {{{\vec V}_{net}}} \right| = \sqrt {({V^2}_L + {V^2}_R)} \\

\left| {{{\vec V}_{net}}} \right| = \sqrt {({i^2}{X^2}_L + {i^2}{R^2})} \\

\\

\]

By taking ${i^2}$ common

\[\left| {{{\vec V}_{net}}} \right| = i\sqrt {({X^2}_L + {R^2})} \]

To calculate the impedance let impedance be $Z$

$Z = \dfrac{V}{i} = \sqrt {({X_L}^2 + {R^2})} $

Because, ${X_L} = \omega L$ we get

$Z = \sqrt {({\omega ^2}{L^2} + {R^2})} $

This is the impedance for series L-R AC circuit

Now, draw the phasor diagram for series L-R AC circuit

$

\tan \varphi = \dfrac{{{V_L}}}{{{V_R}}} \\

\tan \varphi = \dfrac{{i{X_L}}}{{iR}} \\

\\

$

Now, we get

$\varphi = {\tan ^{ - 1}}\left( {\dfrac{{{X_L}}}{R}} \right)$

Therefore, after seeing the phasor diagram we can easily conclude that potential difference across inductance leads the current and potential difference across resistance by an angle $\dfrac{\pi }{2}$

**Hence, option (B) is the correct answer.**

**Note**resistance is the measure of the opposition of current in the circuit. It is denoted by R. It is measured in ohms $(\Omega )$.

Inductance is the property of a conductor to oppose the flow of electric current through it. The flow of current makes a magnetic field around the conductor. It is denoted by L. It is measured in Henry $(H)$.

Last updated date: 02nd Jun 2023

â€¢

Total views: 290.4k

â€¢

Views today: 7.46k

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Ray optics is valid when characteristic dimensions class 12 physics CBSE

A ball impinges directly on a similar ball at rest class 11 physics CBSE

What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?

Alfred Wallace worked in A Galapagos Island B Australian class 12 biology CBSE

Imagine an atom made up of a proton and a hypothetical class 12 chemistry CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

How do you define least count for Vernier Calipers class 12 physics CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Two balls are dropped from different heights at different class 11 physics CBSE