Growth and Decay of Current In LR-Circuit – Complete Notes, Revision, Important Questions & Downloads
Growth and Decay of Current In LR-Circuit is the chapter's standard transient-response block, and this topic is organised through Current Growth When Circuit Closed, Current Decay When Circuit Opened, and Time Constant. The textbook forms are i = i0[1 - e^(-Rt/L)] during growth, i = i0 e^(-Rt/L) during decay, with i0 = E/R and tau = L/R. NEET tests this topic through exponential current reading, 63 percent and 37 percent time-constant facts, and comparisons between initial and steady-state behavior after switching. The main trap is to treat an inductor like a resistor and assume current changes instantly, even though the back emf forces the current to build and fall gradually.
NEET Weightage & Exam Pattern
Electromagnetic Induction| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 1 | 4 | |
| 2022 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2020 | 1 | 4 | |
| Topic Weightage | 5 | 20 |
The time constant is the chapter's favorite conceptual checkpoint because it turns the exponential law into the memorable 63 percent and 37 percent values.
Questions from this topic usually reward careful reading of the switching event more than long algebra, especially at t = 0 and as t tends to infinity.
Preparation Strategy
Identify the Switching Situation First Ask whether the key is being closed onto a battery or opened from a steady-state current. That decision immediately tells you whether the current should rise toward i0 or fall away from it.
Memorise the t = 0 and Long-Time Limits For growth, current starts from zero and approaches E/R. For decay, current starts from the existing steady value and approaches zero. These limits help you reject wrong formulas quickly.
Use Tau as a Physical Time Scale Tau is not just L/R written symbolically. It tells how quickly the current responds, and the 63 percent or 37 percent facts make many MCQs solvable without full substitution.
Keep Exponential Form and Steady Value Separate Do not confuse i0 = E/R with the time-dependent current. The transient formula tells how the circuit approaches that steady value, not what the steady value itself is.
Download Topic Notes
PDF · Cheat Sheet · MCQ Set · PYQTopic Coverage
2-Column TableQuick Revision
Concept → Trap → Example1) Current Growth When Circuit Closed
Rising CurrentWhen a battery is connected to an LR series circuit, current cannot jump instantly to E/R because the inductor opposes the change. The current rises exponentially according to i = i0[1 - e^(-Rt/L)] and approaches the steady-state value i0 = E/R.
- At t = 0, the current is zero because the inductor resists the sudden change.
- As time increases, the exponential term shrinks and the current approaches the steady value E/R.
- Trap: assuming the resistor formula i = E/R applies immediately at the instant of switching.
2) Current Decay When Circuit Opened
Falling CurrentIf an LR circuit is opened after reaching steady state, the current does not vanish immediately. It decays exponentially as i = i0 e^(-Rt/L), showing that the inductor temporarily sustains current by releasing energy stored in its magnetic field.
- At the instant of opening, the current still equals the pre-existing steady value i0.
- As time passes, the exponential factor drives the current toward zero.
- Trap: replacing decay by a linear fall even though the actual transient is exponential.
3) Time Constant
Response ScaleThe time constant of an LR circuit is tau = L/R and has unit second. After one time constant, current reaches 63 percent of its final value during growth or falls to 37 percent of its initial value during decay.
- Larger L makes the response slower because the inductor resists current change more strongly.
- Larger R makes tau smaller, so the transient settles faster.
- Trap: memorising 63 percent and 37 percent without linking them to growth and decay separately.
US Curriculum Gaps
Note for NRI/OCI students studying abroad.Switching Physics Is More Exam-Critical Than Circuit Simulation
Students may have seen RL curves graphically but not be trained to answer one-step questions about what happens immediately after closing or opening the circuit.
- know t = 0 behavior
- know t to infinity behavior
Time Constant Benchmarks Are Used Directly
NEET often expects immediate recall of the 63 percent and 37 percent facts rather than a full derivation from the exponential expression.
- 63 percent during growth
- 37 percent during decay
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Physics Revision Checklist
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Frequently Asked Questions
Notes · Downloads · Revision · Important QuestionsWhy does current grow slowly in an LR circuit?
Why does current not vanish instantly when the circuit is opened?
What is i0 in the LR growth formula?
What is the physical meaning of the time constant?
Why does larger inductance make the response slower?
Why does larger resistance reduce the time constant?
What is the most common mistake in LR-circuit questions?
How does NEET usually test this topic?
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