In an AC circuit with R and L in series which relationship is true

This question was previously asked in

IPRC (ISRO) Technical Assistant (Electronics): Previous Paper 2018 (Held On: 21 April 2018)

Option 4 : the voltage across the resistor lags the voltage across the inductor by 90 degree

CT 1: Basic Concepts

18320

10 Questions
10 Marks
6 Mins

In an AC circuit with R and L in series, the voltage across the resistor lags the voltage across the inductor by 90 degrees.

__Resistance__: If only a resistive element is present in the circuit, then the current is in phase with the voltage, i.e.

**V** =** I** R

__Inductance__: If the pure inductive element is present in the circuit, then the current lags the voltage by 90 degrees, i.e.

**V** = **I** jωL

**V = I ∠90°L**

Now, for an RL series circuit, we can write:

**V _{R}** =

\(I=\frac{V_R}{R}\) ---(1)

**V _{L}** = I ∠90°L

Using Equation (1), we can write:

\(V_L=\frac{V_R}{R}\times L\angle 90^o\)

\(V_R=\frac{V_L\times R}{L}\angle -90^o\)

∴ The voltage across the resistor lags the voltage across the inductor by 90 degrees.

__Capacitance__:

- If the pure capacitive element is present in the circuit, then the current leads the voltage by 90 degrees.
- The power factor, in this case, is leading.