Question

In a series LCR CIRCUIT resistance $R=10\Omega $ and the impedance $Z=10\Omega $. The phase difference between the current and the voltage is:
A) 0
B) 30
C) 45
D) 60

Answer 1

Hint: Firstly, we should have a basic idea about the LCR circuit, what is phase difference because the concept used in this question is a phase difference in the LCR circuit. We find impedance and then using the formula of phase difference we will find the answer.

Formula used:
\[z=\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}\]
\[\tan \phi =\dfrac{{{X}_{L}}-{{X}_{C}}}{R}\]

Complete answer:
Given, resistance of the LCR circuit, $R=10\Omega $
Given, impedance of the LCR circuit, $Z=10\Omega $
We know the formula of impedance ,
\[\begin{align}
  & z=\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}} \\
 & \therefore 10=\sqrt{{{10}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}} \\
 & \Rightarrow 100=100+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}} \\
 & \Rightarrow {{X}_{L}}-{{X}_{C}}=0 \\
\end{align}\]
Let us assume \[\phi \] is the phase difference between current and voltage .
 We know that;
\[\tan \phi =\dfrac{{{X}_{L}}-{{X}_{C}}}{R}\]
\[\because {{X}_{L}}-{{X}_{C}}=0\]
\[\therefore \tan \phi =\dfrac{0}{R}\]
\[\Rightarrow \phi =0\]
The obtained phase difference between the current and the voltage is 0.

So, the correct answer is “Option A”.

Additional Information:
To describe the difference in degrees or radians when two or more alternating quantities reach their maximum or zero values, phase difference is used. Previously we saw that a Sinusoidal Waveform is an alternating quantity that can be presented graphically in the time domain along a horizontal zero axis.

Note:
The effective resistance of the series LCR circuit which opposes or resists the flow of current through it is known as its impedance. The relationship between the resistance, inductive resistance, capacitive resistance, and impedance in LCR makes a right-angled triangle graphically, known as the impedance triangle.