Question

At resonance, what is the relation between impedance of LCR circuit and its resistance R?

Answer 1

In order to answer this question, we know that An LCR circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel and impedance is the measure of the resistance that a circuit exerts to current with the application voltage.

Complete step-by-step solution:

Resonance is the phenomenon in the circuit when the output of that electric circuit is maximum at one particular frequency. In an LCR circuit, this frequency is determined by the values of inductance, conductance, and resistance. If the inductor, capacitor and resistor are connected in series then the circuit is called a Series resonance circuit. But, if they are connected in parallel, then the circuit is called Parallel Resonance circuit.
In LCR series circuits,
As we know that at resonance,
${X_L} = {X_c}$
Where as
${X_L}{\text{ is the inductive reactance}} \\\ {X_C}{\text{ is the capacitive reactance}}$
So, total reactance is ${X_T}$ which is,
${X_T} = {X_L} - {X_C}$
Which is Zero
$\therefore Z = \sqrt {{{({X_{_L}} - {X_C})}^2} + {R^2}} \\\ \Rightarrow Z = \sqrt {{R^2}} \\\ \Rightarrow Z = R$
$Z$ is impedance.
$R$ is resistance
So, the relation between impedance of a series LCR circuit and its resistance R at resonance is $Z = R$
Additional Information:
Inductor (L): It is a two-terminal passive electrical component that opposes sudden changes in current. It is used to store energy in the form of magnetic energy when electricity is applied to it.
Capacitor(C): A capacitor is a two-terminal electrical device that can store energy in the form of an electric charge. Capacitors include two electrical conductors, which are separated by a distance.
Resistor(R): A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses.

Note: Impedance can be minimized by making the applied AC frequency equal to the resonant frequency of the LCR circuit. There is no difference between an RLC circuit and an LCR circuit except for the order of the symbol represented in the circuit diagram.