GATE EE 2023 Set 1 — Question 54
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0HardTransient Response (DC & AC)Transient & AC Steady-StateElectric Circuits
Electric Circuits → Transient & AC Steady-State → Transient Response (DC & AC)
Last updated
Question
The circuit shown in the figure is initially in the steady state with the switch in open condition and in closed condition. The switch is closed and is opened simultaneously at the instant , where . The minimum value of in milliseconds, such that there is no transient in the voltage across the capacitor, is ____________ (Round off to 2 decimal places).
Correct answer
1.56 to 1.58
Solution
1.Initial State ():
The switch is open and is closed. The circuit has reached steady state. The capacitor is connected to the DC source through a resistor. In steady state, the capacitor acts as an open circuit.2.Final State ():
Switch is closed and is opened. The capacitor is now in parallel with a resistor and a current source .3.Steady-State Response for :
The equivalent impedance of the parallel combination is:Given , , and :
The steady-state capacitor voltage is:
4.Condition for No Transient:
For no transient to occur, the initial voltage on the capacitor at the switching instant must exactly match the steady-state value at that same instant:5.Solving for :
The minimum positive value for occurs when:In milliseconds, .(Note: The derivative condition is also satisfied at this point, ensuring a completely transient-free transition.)
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Transient & AC Steady-State
2026 Set 1 Q23A circuit with ideal elements is shown. [figure] Which one of the following options correctly…2026 Set 1 Q24For the circuit shown, which one of the following options correctly identifies the Thevenin’s…2026 Set 1 Q25Refer to the four circuits shown. Which one of the following options for and …2026 Set 1 Q26A single-phase voltage source V delivers a current,…2026 Set 1 Q42An electrical component has voltage drop , when the current through it is…