Question

At resonant frequency the current amplitude in series LCR circuit is:
A. maximum
B. minimum
C. zero
D. infinity

Answer 1

Hint: To solve this question, i.e., to find the current amplitude in the LCR circuit, whether it will be maximum, minimum, zero or infinity. So, we will start with taking impedance across an LCR circuit. Z will be minimum as the impedance is minimum at resonant frequency. Now, applying the formula of current amplitude across the LCR circuit, we will have the required answer.

Complete step by step answer:
In the question, we are asked about the current amplitude in series LCR circuits at resonant frequency.
At first, we will start with taking impedance, using the formula mentioned below.
Impedance, $Z = \sqrt {{R^2} + ({X_L} - {X_C})} $
where, Z \[ = \] Impedance across the circuit
R \[ = \] Resistance across the circuit
XL \[ = \] Inductive reactance across the circuit
XC \[ = \] Capacitive reactance across the circuit
At resonant frequency, \[{X_C} = {X_L}\], i.e., Inductive reactance \[ = \] Capacitive reactance
From the above formula, we get
$\begin{gathered}
  Z = \sqrt {{R^2}} \\
  Z = R \\
\end{gathered} $
So, Z is minimum. (Because from the formula rest of the value is zero at resonant frequency)
Now, we need to find the current amplitude in the series LCR circuit.
We know that, \[{I_0} = \dfrac{{{V_0}}}{Z}\]
where, ${I_0} = $ maximum current
${V_0} = $ Voltage
$Z = $ Impedance
Already mentioned earlier that, at resonant frequency, Z \[ = \] minimum.
Now from the above formula, we get
$ \Rightarrow {I_0} = $ maximum

So, the correct answer is “Option A”.

Note:
Here, in the question we have been given a circuit called LCR, let us understand about this circuit in detail. LCR circuit also called as RLC circuit, is an electric circuit consisting of an inductor (L), a capacitor (C) and a resistor (R), connected in series or in parallel.