Physics · Class 12

Series LCR resonance

Near resonance, inductive and capacitive reactances cancel. Resistance limits the current and controls peak width; small resistance makes a sharper resonance.

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Series LCR resonance

ஒத்ததிர்வில் சுருள் மற்றும் தேக்கி மறுமின்தடைகள் ரத்தாகும். மின்தடை மின்னோட்டத்தை வரையறுக்கும்.

Key notes, relationships and model limits

Key relationship

f₀=1/(2π√LC); Zminimum=R; Imaximum=Vrms/R.

Remember

Near resonance, inductive and capacitive reactances cancel. Resistance limits the current and controls peak width; small resistance makes a sharper resonance.

Common trap

At series resonance XL = XC and Z = R. The individual inductor and capacitor voltages need not vanish.

Model limits

Ideal driven series LCR; finite positive R avoids unbounded current.

What you will learn

Use the controls and plotted relation to explain series lcr resonance.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

L=100 mH and C=100 µF give f₀≈50.33 Hz.

Why this matters

The model connects series lcr resonance with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

At series resonance, current is?

Zero because inductive and capacitive currents disappear.
Maximum for a fixed supply amplitude.
Minimum for a fixed supply amplitude.

Read the explanation

Maximum for a fixed supply amplitude.

Course connection: Class XII Chapter 7. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.