Eigenvalues and eigenvectors of a 2 × 2 matrix
Use a characteristic equation to understand matrix eigenvalues, then verify the result by multiplication.
Read worked solution →Worked examples by subject
Unlike a syllabus checklist or scanned paper, these pages teach a specific calculation and explain why the method works. Start with a subject, try the question on your own, and reveal the solution only after attempting it.
New worked practice test: Network Theory — Set 01 now includes 17 rephrased questions, 16 custom circuit and concept diagrams, an answer key, and detailed explanations. Open the complete test →
RC charging transient and time constant
Predict capacitor voltage after switching and determine when a specified charging percentage is reached.
Read worked solution →Capacitance and electric field in a coaxial cable
Apply Gauss’s law to a cylindrical geometry and connect electric-field strength with capacitance.
Read worked solution →Convolution of two causal exponential signals
Solve a continuous-time LTI response by convolution and verify the answer with Laplace transforms.
Read worked solution →Induction motor slip, rotor frequency and power
Turn speed and air-gap power information into rotor copper loss and converted mechanical power.
Read worked solution →Per-unit impedance and change of base
Calculate base impedance and current, then convert a line reactance between system bases.
Read worked solution →Second-order closed-loop response from a transfer function
Extract damping ratio, natural frequency, overshoot and settling time without plotting software.
Read worked solution →Voltmeter full-scale accuracy and loading error
Separate instrument tolerance from circuit disturbance when estimating voltage measurement accuracy.
Read worked solution →Non-inverting op-amp gain and bandwidth
Connect resistor feedback to amplifier gain, estimate bandwidth, and test the limits of an ideal model.
Read worked solution →Buck converter duty cycle and inductor ripple
Calculate output voltage, inductor current ripple and the continuous-conduction boundary.
Read worked solution →Nodal analysis with two unknown nodes
Write KCL equations, solve simultaneous equations and verify currents.
Read worked solution →Thevenin equivalent and load power
Calculate open-circuit voltage, equivalent resistance and maximum power.
Read worked solution →Transparency: These newly drafted examples are AI-assisted educational material. They are not copied GATE question papers, nor are they claimed as original GATE examination questions. An educator should review the drafts before publishing them and continue adding verified lesson material.