An RLC series circuit has R = 56 Ω , X_L = 64 Ω , and X_C = 37 Ω . What is the value of Z?

A) 25.49 Ω
B) 43 Ω
C) 59 Ω
D) 62.17 Ω

The total impedance (Z) in an RLC series circuit is calculated using the formula $Z=\sqrt{R^2+(X_L-X_C{)}^2}$ , where $R$ is the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance. Substituting the given values, $Z=\sqrt{56^2+(64-37{)}^2}=\sqrt{3136+729}=\sqrt{3865}=62.17\Omega$ .