Recall resonance condition

In a series RLC circuit, resonance occurs when the inductive reactance $X_L$ equals the capacitive reactance $X_C$.

$X_L = X_C$

Define Impedance formula

The general impedance $Z$ for a series RLC circuit is determined by resistance $R$ and the difference between reactances.

$Z = \sqrt{R^2 + (X_L - X_C)^2}$

Substitute resonance condition

Substitute $X_L = X_C$ into the impedance formula to find the value at resonance.

$Z = \sqrt{R^2 + (0)^2} = R$

Calculate result

Since $R = 50 \Omega$, the impedance $Z$ is equal to $50 \Omega$.

$Z = 50 \Omega$