Question

using phasor diagram, find an expression of impedance of a series lcr circuit. also find the condition for resonance of series lcr circuit.

Answer 1

The impedance of an RLC series circuit is calculated using the expression Z = √(R² + (XL - XC)²). Resonance occurs when inductive and capacitive reactances equal each other, and the resonant frequency is given by fo = 1 / (2π√(LC)).

Step-by-step explanation:

Calculating the impedance of a series RLC circuit, involves combining the resistance (R), inductive reactance (XL), and capacitive reactance (XC) into a single entity. The expression for impedance (Z) is given by Z = √(R² + (XL - XC)²).

Here, XL = 2πfL and XC = 1 / (2πfC), where f is the frequency, L is the inductance, and C is the capacitance. For resonance to occur in a series RLC circuit, the inductive and capacitive reactances must be equal, cancelling each other out, thus XL = XC and Z becomes minimal, equal to just R.

The resonant frequency (fo) is found by setting XL = XC and solving for f.

Using the formula fo = 1 / (2π√(LC)), you can determine the frequency at which resonance occurs.