Which of the following circuits will have transients ? 1. Resistive Which is correct ?
2. R-L
3. R-C
4. R-L-C
2, 3, 4
A transient requires an element that stores energy, and a purely resistive circuit has none — so the answer is 2, 3 and 4, option 4.
Why a resistive circuit cannot have a transient. Ohm's law is algebraic:
\(i=\dfrac{v}{R}\)
The current at any instant depends only on the voltage at that instant. There is no derivative, so there is no differential equation to solve, no time constant, and no memory of what came before. Apply a step and the current steps with it — the new state is reached immediately.
Why the other three do have transients. Each contains at least one storage element whose defining relation involves a derivative:
| Element | Relation | Cannot change instantly |
|---|---|---|
| Inductor | \(v=L\dfrac{di}{dt}\) | Its current |
| Capacitor | \(i=C\dfrac{dv}{dt}\) | Its voltage |
A discontinuous change would demand infinite voltage or infinite current. Energy stored as \(\frac{1}{2}Li^{2}\) or \(\frac{1}{2}Cv^{2}\) must be moved at a finite rate, and the interval during which it is redistributed is the transient.
The order of the circuit sets the character of the response.
First order — R-L or R-C, one storage element — gives a simple exponential with a single time constant, \(\tau=L/R\) or \(RC\). It approaches the final value monotonically and can never overshoot.
Second order — R-L-C, two storage elements — allows energy to be exchanged between L and C, so the response can oscillate. Its character depends on the damping:
\(\zeta=\dfrac{R}{2}\sqrt{\dfrac{C}{L}}\qquad\text{(series R-L-C)}\)
giving an overdamped, critically damped or underdamped approach — the last with ringing at
\(\omega_{d}=\omega_{n}\sqrt{1-\zeta^{2}}\)
Where this matters practically : stray inductance and capacitance are unavoidable, so every real "resistive" circuit shows a small transient at high enough speed — which is why fast digital edges ring on long traces.
Hence, the circuits with transients are 2, 3 and 4.
Similar Questions
For series RLC circuit given below in figure, choose the correct answer based on Kirchoff's voltage law from following:
The RLC circuit given in figure below can be solved
A. Current i(t) can be solved using KVL
B. Current i(t) can be solved using KCL
C. Current i(t) can be solved using fourier transform
D. Current i(t) can be solved using laplace transform
E. Current i(t) can be solved using Fourier series
Choose the correct answer from the options given below:
Match the following in the context of RLC series circuit :
List - I List - II (a) Under damped (i) \(\xi=1\) (b) Critically damped (ii) \(\xi \gt 1\) (c) Quality factor (iii) \(\dfrac{1}{2\xi}\) (d) Over damped (iv) \(\xi \lt 1\) Codes :
Important Questions from Transient Analysis
Consider the following statements regarding circuit elements:
1. The voltage across a capacitor cannot change instantaneously.
2. The current through an inductor cannot change instantaneously.
3. The current through a capacitor is always a continuous function.
4. The voltage across an inductor is always a continuous function.
Which of these statements are correct?
At t = 0+ an inductor with zero initial condition acts as a/an
During discharging of a capacitor of C = 100 µF through a resistance of 1 KΩ applied with 50 V, the voltage at the time of the it's time constant is
Name that transient which is produced when a circuit, which is originally dead, is energized.
What is the value of current at t = 5T instant in an RC network fed with voltage V where T is time constant?
