Final answer:
To determine the capacitive reactance (X_C) in an AC series circuit at resonance, calculate the inductive reactance (X_L = 2πf_rL) using the given resonant frequency and inductance. At resonance, X_L equals X_C.
Step-by-step explanation:
To find the value of the capacitive reactance X in an AC series circuit at resonance, we must remember that at resonance, the inductive reactance (XL) is equal to the capacitive reactance (XC), thereby cancelling each other out. The formula for inductive reactance is XL = 2πfrL, and for a circuit at resonance, XL is equal to XC.
Given the resonant frequency fr = 2.45 kHz and the inductance L = 155 nH, the inductive reactance at resonance can be calculated as follows:
XL = 2π × 2450 Hz × 155 x 10-9 H.
Calculating this gives us the inductive reactance, which is equal to the capacitive reactance at resonance. Therefore, the capacitive reactance XC will have the same value.