EEE PYQ Derivations

eee-1109 EEE-1109 Basic Electrical Engineering

1. DC Circuit Analysis and Network Theorems

Question / Derivation Task	Year(s) of Appearance
Deduce the condition for maximum power transfer.	2016, 2018, 2019, 2022, 2023
Show that power transfer efficiency is 50% under the maximum power transfer condition.	2016, 2018, 2019, 2022
Deduce the expression for Y-$\Delta$ and $\Delta$-Y conversions of a resistive network.	2018, 2022
Derive the node voltage equations (and determine the current in each branch).	2018

2. Magnetic Circuits and Coupling

Question / Derivation Task	Year(s) of Appearance
Show that the magnetic flux density at any specified distance from a long straight current-carrying conductor is $B=\mu I/2\pi r$.	2016
Derive the expression of the coefficient of magnetic coupling.	2016, 2019, 2023
Show that the maximum value of the coefficient of magnetic coupling could be unity.	2023
Derive the expression of energy stored in a toroid.	2016
Show that the energy stored in a toroid is $W=1/2B^{2}l/{\mu }_0$.	2016

3. AC Fundamentals and Power

Question / Derivation Task	Year(s) of Appearance
Show that the crest factor of a sine wave is $\sqrt{2}$ and the form factor is 1.11.	2016, 2018
Show the expression of energy delivered and received for purely inductive and capacitive branches respectively for a quarter cycle.	2016, 2017, 2018
Show that the average power consumed by inductance or capacitance is zero (or “power absorbed in a pure capacitor is zero”).	2017, 2023
Write the equation of instantaneous power of an RL branch and show its different components graphically.	2019, 2022
”Multiplication and division operations of phasors are suitable in polar form” — justify the statement.	2018

4. AC Resonance

Question / Derivation Task	Year(s) of Appearance
Prove that “In RLC series circuit the maximum voltage across the capacitor occurs below the resonant frequency and the maximum voltage across the inductor occurs above the resonant frequency”.	2016, 2019, 2022
Derive the expression for bandwidth of a series RLC selector circuit.	2018, 2019
”The frequency range for the pass band is $\Delta f=R/2\pi L$ for a RLC series circuit” — justify this.	2017
Derive the Q-factor, $Q_0=f_{0}L/R$.	2018
Determine (derive) the resonant frequency formula for an RLC series circuit.	2023

5. Three-Phase Systems

Question / Derivation Task	Year(s) of Appearance
Prove that a $3\Phi$ system is more economical than a $1\Phi$ and $4\Phi$ system respectively.	2016, 2017, 2018
Show the voltages and currents relation for a star-connected $3\Phi$ system using a vector diagram.	2022, 2023
Explain the two-wattmeter method of measuring power of a $3\Phi$ system (with derivations).	2018, 2023, 2024