Which one of the following curves represents the variation of impedance (Z) with frequency f in series LCR circuit?

Concept:

In a series LCR circuit, the impedance (Z) depends on the inductive reactance (X_L) and capacitive reactance (X_C), and it varies with the frequency (f) of the alternating current. Impedance can be calculated using the formula:

Z = √(R² + (X_L - X_C)²)

Where,

• R is the resistance
• X_L = 2πfL (Inductive reactance)
• X_C = 1/(2πfC) (Capacitive reactance)

Calculation:

At resonance frequency (f₀), X_L = X_C, so impedance Z is minimum and equals R.

For frequencies below resonance (f < f₀):

⇒ X_L < X_C

⇒ Z increases as f decreases.

For frequencies above resonance (f > f₀):

⇒ X_L > X_C

⇒ Z increases as f increases.

Hence, the curve representing Z vs. f will have a minimum at resonance frequency and will rise on both sides of this frequency.

The correct curve that represents the variation of impedance (Z) with frequency (f) in a series LCR circuit is option 3.

∴ The correct answer is option 3.