Question

The power factor of an AC circuit is 0.5 what is the phase difference. What is the phase difference between voltage and current in the circuit?.

Answer 1

Hint: The phase difference between voltage and current varies for RC and RL circuits. In a resistor the phase difference between voltage and current are in phase. In the RC circuit the current leads the voltage and in the RL current lags the voltage. In the inductor we consider current whereas in the capacitor we consider voltage.

Complete step-by-step solution:
When the capacitor or inductor are present in an AC circuit. The current and the voltage cannot peak at the same time. The fraction of a period difference between the peaks expressed in degree is said to be the phase difference .In an inductive circuit the current lags the voltage and in a capacitive circuit the current leads the voltage.
Phasor diagram of $RLC$ circuit

The phasor diagram of the $RLC$ series circuit when the circuit as an inductive circuit means$({{V}_{L}}>{{V}_{C}})$ is shown below and if $({{V}_{L}}<{{V}_{C}})$ the circuit will behave as a capacitive circuit.
$V=\sqrt{{{V}_{R}}^{2}+{{({{V}_{L}}-{{V}_{C}})}^{2}}}$
$\phi ={{\tan }^{-1}}\dfrac{{{V}_{L}}-{{V}_{C}}}{{{V}_{R}}}$
$impedance(z)=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}$
$phase angle(\phi )={{\tan }^{-1}}\dfrac{{{X}_{L}}-{{X}_{C}}}{R}$
Power factor in AC circuit is given by:
$\cos \phi =\dfrac{V}{I}$
Where $V$ = True voltage
              $I$ = Current
             $\phi $ = Phase difference between voltage and current
From the data
$\cos \phi =0.5$
$\phi ={{\cos }^{-1}}(0.5)={{60}^{0}}$
The phase difference between voltage and current is ${{60}^{0}}$.

Note:In a pure ohmic resistance, the current and voltage are both in phase as there is no phase difference between them. The current flows through the resistance is directly proportional to the voltage across it with this linear relationship in an AC circuit being called impedance and the indian standard frequency is 50Hz.