Key relationship
RC: Vc=V(1−e⁻ᵗ/ᴿᶜ); LR: I=V/R(1−e⁻ᴿᵗ/ᴸ); LC: Vc=Vcos(t/√LC).
Physics · Class 12
RC, LR and LC transients
Switch among capacitor charging, inductor current rise and ideal energy exchange in an LC circuit. RC and LR approach a steady state; ideal LC continues oscillating.
Open the interactive experiment →RC, LR and LC transients
RC-இல் தேக்கி மின்னழுத்தம் உயர்கிறது. LR-இல் மின்னோட்டம் உயர்கிறது. LC-இல் ஆற்றல் மின்புலத்துக்கும் காந்தப்புலத்துக்கும் மாறுகிறது.
Key notes, relationships and model limits
Remember
Switch among capacitor charging, inductor current rise and ideal energy exchange in an LC circuit. RC and LR approach a steady state; ideal LC continues oscillating.
Common trap
RC and LR approach a DC steady state; ideal LC keeps exchanging energy. Resistance would damp that ideal LC oscillation.
Model limits
Ideal initial conditions: RC uncharged, LR zero current, LC initially charged with zero current. LR voltage readout is across the inductor; LC has no resistance.
What you will learn
Use the controls and plotted relation to explain rc, lr and lc transients.
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
With R=100 Ω and C=100 µF, τ=0.01 s; after τ, a 12 V source gives Vc≈7.585 V.
Why this matters
The model connects rc, lr and lc transients with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
After one RC time constant, a charging capacitor voltage is approximately?
- 36.8% of supply voltage.
- 63.2% of the supply voltage.
- 100% of supply voltage.
Read the explanation
63.2% of the supply voltage.
Course connection: Class XII Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.