GATE ECE Electrical Networks notes
State the circuit reference directions and element assumptions before applying KCL, KVL or equivalent-circuit methods.
BEFORE YOU BEGIN
Start with the right foundations
Algebra, complex numbers, differential equations and passive-sign convention.
Original introductory notes with source references. The example is a teaching exercise, rather than an official worked solution to a GATE question. Use the full syllabus to track coverage.
01 · UNDERSTAND
Key concepts
Use these ideas to reason through a question before choosing a formula or an answer.
Circuit laws
KCL balances currents at a node; KVL balances voltages around a loop under the lumped-circuit model. A negative result means the actual direction is opposite to the reference you chose.
Equivalent sources
For a linear two-terminal network, Vth is open-circuit voltage and Rth is the equivalent resistance with independent sources suppressed. Dependent sources remain active; a test source may be needed.
First-order transients
An RC time constant is R_eq C with R_eq seen by the capacitor. For a stable first-order step, vC(t) = vC(∞) + [vC(0+) − vC(∞)] exp(−t/τ). Capacitor voltage is continuous unless an ideal impulse current is applied.
02 · WORK THROUGH IT
A worked teaching example
Attempt the problem first, then trace each step and compare your reasoning.
The problem
An initially uncharged 1 μF capacitor is connected through 1 kΩ to an ideal 5 V DC source at t = 0. Find its voltage at t = 1 ms.
Step-by-step reasoning
- 1
The time constant is 1,000 × 10^−6 = 0.001 s = 1 ms.
- 2
Initial voltage is 0 V and final voltage is 5 V.
- 3
At one time constant, vC = 5(1 − exp(−1)).
Check your result
Compare your calculation and assumptions.
Approximately 3.16 V.
03 · SPOT THE TRAPS
Common mistakes
- Suppressing dependent sources while calculating equivalent resistance.
- Confusing capacitor voltage continuity with resistor voltage continuity.
- Mixing μF and F.
04 · CHECK YOUR UNDERSTANDING
Revision checklist
- Mark current and voltage references.
- Find initial and final conditions.
- Check the time constant dimensions.
Explain each point without the notes, then check it with an unfamiliar question. Print or save these notes as a PDF for your revision session.
05 · APPLY IT
Put these ideas into practice
Attempt related previous year questions and record the reasoning behind any mistakes.
Explore the archive to find a related topic for your next practice session.
Plan your next revision session
Explore topic history or move to another note.
READ FURTHER
Study references
Use the original references for a fuller explanation and more worked problems.