BE Computer Engineering (Pokhara University) Basic Electrical Engineering (PU, ELE 120) Question Paper 2078

(a) Define the following terms with neat sketches: node, branch, loop and mesh of an electric network. State Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). (4)

(b) For the circuit shown below, determine the current flowing through the $10\,\Omega$ resistor using mesh (loop) analysis. The circuit consists of two voltage sources $E_1 = 20\,\text{V}$ and $E_2 = 12\,\text{V}$ connected through resistances $R_1 = 4\,\Omega$, $R_2 = 6\,\Omega$ and a common middle branch $R_3 = 10\,\Omega$. (6)

(c) Verify the result obtained in part (b) using nodal analysis by taking the junction between $R_1$, $R_2$ and $R_3$ as the principal node. (4)

(a) State Thevenin's theorem and explain, with the help of suitable diagrams, the step-by-step procedure to obtain the Thevenin equivalent circuit of a linear two-terminal network. (5)

(b) A network has a load resistance $R_L$ connected across terminals A-B. The rest of the network, when the load is removed, presents an open-circuit voltage of $24\,\text{V}$ and a Thevenin resistance of $8\,\Omega$ across A-B. Determine the value of $R_L$ for which maximum power is transferred to the load, and calculate this maximum power. (5)

(c) Hence, derive an expression for the efficiency of power transfer under maximum-power-transfer conditions and comment on its value. (4)

(a) Explain the working principle and constructional features of a single-phase transformer with a neat labelled diagram. (4)

(b) Derive the EMF equation of a single-phase transformer, clearly stating all assumptions. (5)

(c) A $25\,\text{kVA}$, $2200/220\,\text{V}$, $50\,\text{Hz}$ single-phase transformer has iron losses of $350\,\text{W}$ and full-load copper losses of $450\,\text{W}$. Calculate (i) the efficiency at full load and $0.8$ power factor lagging, and (ii) the load (as a fraction of full load) at which maximum efficiency occurs. (5)

(a) For a balanced three-phase star (Y) connected system, derive the relationship between line and phase voltages and between line and phase currents. Repeat the derivation for a balanced delta (Δ) connected system. (6)

(b) A balanced three-phase star-connected load draws a line current of $15\,\text{A}$ from a $400\,\text{V}$ (line), $50\,\text{Hz}$ supply at a power factor of $0.85$ lagging. Calculate the total active power, reactive power and apparent power consumed by the load. (4)

(c) Briefly explain the two-wattmeter method of measuring three-phase power and state how the load power factor can be obtained from the two wattmeter readings. (2)

A series RLC circuit consists of $R = 10\,\Omega$, $L = 0.1\,\text{H}$ and $C = 50\,\mu\text{F}$ connected across a $230\,\text{V}$, $50\,\text{Hz}$ supply. Determine (a) the impedance of the circuit, (b) the current drawn and its phase angle with respect to the applied voltage, and (c) the resonant frequency of the circuit.

(a) Define average value and RMS value of an alternating quantity, and derive the form factor for a sinusoidal waveform. (3)

(b) Explain the meaning of power factor in an AC circuit. Why is a low lagging power factor undesirable in power systems? (3)

(a) Draw the analogy between an electric circuit and a magnetic circuit, listing the corresponding quantities. (3)

(b) An iron ring of mean circumference $40\,\text{cm}$ and cross-sectional area $5\,\text{cm}^2$ has a relative permeability of $500$. It is wound with $200$ turns carrying a current of $2\,\text{A}$. Calculate the reluctance of the magnetic circuit and the flux produced in the ring. (3)

(a) Derive the EMF equation of a DC generator. (3)

(b) A 4-pole DC shunt generator has a lap-wound armature with $440$ conductors. It is driven at $1000\,\text{rpm}$ and the flux per pole is $25\,\text{mWb}$. Calculate the generated EMF. (3)

(a) Explain the working principle of a DC motor and state the significance of back EMF. (3)

(b) A DC shunt motor connected to a $220\,\text{V}$ supply draws an armature current of $20\,\text{A}$. If the armature resistance is $0.5\,\Omega$, determine the back EMF developed and the electrical power converted into mechanical power. (3)

(a) With a neat diagram, explain the construction and working of a permanent-magnet moving-coil (PMMC) instrument. (3)

(b) Distinguish between PMMC and moving-iron (MI) instruments on the basis of nature of scale, type of current measured, and damping employed. (3)

(a) Explain how the range of a moving-coil ammeter is extended using a shunt and how a voltmeter range is extended using a series multiplier resistance. (3)

(b) A moving-coil galvanometer has a resistance of $50\,\Omega$ and gives full-scale deflection at $1\,\text{mA}$. Calculate the value of shunt resistance required to convert it into an ammeter reading up to $1\,\text{A}$. (3)

State the superposition theorem and explain its limitations. Using the superposition theorem, find the current through a $5\,\Omega$ resistor in a circuit energised simultaneously by a $10\,\text{V}$ voltage source (in series with $2\,\Omega$) and a $4\,\text{A}$ current source, both feeding the common $5\,\Omega$ branch.