RL and RC Transients with Stored Energy
The RL time constant is L/R and the RC time constant is RC. After one time constant, a growing quantity reaches about 63 percent and a decaying quantity retains about 37 percent.
Why this shows up in the exam
Relay delay circuits · Camera-flash charging · Current and voltage smoothing
Learn the idea
Inductors and capacitors make circuit changes gradual and store field energy. An inductor prevents an instantaneous change of current; a capacitor prevents an instantaneous change of voltage. Their responses grow or decay exponentially.
🧠 Memory hook: One tau: 63 up, 37 left.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau_L = L/R — RL time constant
- tau_C = R C — RC time constant
- x_growth = x_final(1 - e^(-t/tau)) — generic first-order growth
- U_L = (1/2) L I²; U_C = (1/2) C V² — stored magnetic and electric energy
How to approach it
- 1Identify whether L or C controls the transient
- 2Find initial and final values
- 3Choose the correct time constant and growth or decay form
Common slip-ups that cost marks
- •Interchanging L/R and RC
- •Allowing inductor current or capacitor voltage to jump
- •Using LI squared or CV squared without the one-half
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
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