Electronics Engineering (ELEX) Board Practice Exam

What happens to the impedance in a series RLC circuit at resonance?

1. It becomes zero

2. It becomes purely resistive

3. It becomes capacitive

4. It becomes inductive

The correct answer is: It becomes purely resistive

At resonance in a series RLC circuit, the impedance becomes purely resistive. This occurs when the inductive reactance (due to the inductor) and capacitive reactance (due to the capacitor) are equal in magnitude but opposite in phase. As a result, they cancel each other out. The overall impedance of the circuit is then determined solely by the resistance (R) in the circuit. In mathematical terms, at resonance, the inductive reactance (XL) can be expressed as XL = 2πfL, and the capacitive reactance (XC) as XC = 1/(2πfC), where f is the frequency. When these two reactances are equal (XL = XC), the total impedance (Z) of the series circuit simplifies to just the resistance value (R), which is why it is termed "purely resistive." This has important implications for the behavior of the circuit, as at resonance, the circuit can achieve maximum current flow for a given applied voltage due to the lower impedance. The resonance condition dramatically affects how the circuit responds to different frequencies, making it crucial in applications like tuning circuits and filters.