Question

What can you say about the impedance of a series RLC circuit at the resonant frequency? The impedance of a series RLC circuit is maximum in magnitude at the resonant frequency and is equal to the resistance.

Answer 1

Answer:

At resonance impedance of series RLC circuit is minimum and equal to resistance of the circuit

Explanation:

Let the resistance of the series RLC circuit is R

Capacitive reactance of the circuit is $X_C$ and inductive reactance of the circuit is $X_l$

We know that impedance of the series RLC circuit is given by $Z=\sqrt{R^2+(X_L-X_C)^2}$, here R is the resistance $X_l$ is inductive reactance and $X_C$ is capacitive reactance

At resonance capacitive reactance will be equal to inductive reactance

So $X_C=X_l$

So impedance will become $Z=R$

So from above calculation we can say that impedance of series RLC circuit is minimum and equal to resistance of the circuit

Answer 2

Answer:

Explanation:

Let R is the resistance of the circuit, L is the inductance of the circuit and c is the capacitance.

Inductive reactance= XL

capacitive reactance = Xc

The impedance of the RLC circuit is

$Z=\sqrt{R^{2}+\left ( X_{L}^{2}-X_{C}^2 \right )}$

As the circuit is in resonance, So, XL = Xc

In this condition, Z = R

So, the impedance is equal to the resistance of the circuit.