## Basic Electrical Engineering (BEE) - May 2014

### First Year Engineering (Semester 1)

TOTAL MARKS:

TOTAL TIME: HOURS

### Answer any one question from Q1 and Q2

**1 (a)** With usual notations: derive the relationship, $$\alpha_2 = \dfrac {a_1}{1+\alpha_1 (t_2-t_1)} $$ And hence obtain $$ i) \ \ a_t = \dfrac{a_0}{1+a_0t} \\ i) \ \ a_0 = \dfrac {a_t}{1-a_t t} $$(6 marks)
**1 (b)** A coil of N turns is wound on a cast iron ring which has mean length of 50 cm and its cross-section is of 4 cm diameter. The
current flowing through the coil is 2 A which produces a flux
Of 6 nWb in the air-gap of 2mm length. If the relative permeability of iron is 1000, calculate the number of turns N.(6 marks)
**2 (a)** With reference to a magnetic circuit explain the teRMS-i) magnetic flux, ii) magneto-motive force, iii) magnetic field intensity, iv) magnetic flux density, v) reluctance, vi) permeability of free space. State their units.(6 marks)
**2 (b)** A pump driven by a DC electric motor lifts 1.5 m^{3} of water per minute to a height of 40 m.
The pump has an efficiency of 90 % and the motor an efficiency of 85%. Determine (i) the power input to the motor, (ii) the current taken from a 480 V supply. Assume the mass of one m^{3} of water is 1000 kg.(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Draw neat sketches to show core-type and shell-type single phase transformers. State:

i) losses occurring in the transformer on load.

ii) their location, cause, whether constant or variable.

iii) factors on which they depends(6 marks)
**3 (b)** A series of combination having R= 2MΩ and C= 0.01 μF is connected across the DC source of 50 V. Determine the capacitor voltage and charging current after 0.02s and 0.06s.(6 marks)
**4 (a)** Derive an expression for instantaneous current and power consumed when voltage of V= V_{m }Sin (wt) is
applied to pure inductance alone. Also draw the phasor diagram.(6 marks)
**4 (b)** A transformer is rated at 100 KVA. At full load, its copper loss is 1200 W and its iron loss is 960 W. Calculate:

(i) Efficiency at full load, 0.8 power factor,

ii) Load KVA at which maximum efficiency will occur.

(iii) Maximum efficiency at 0.85 power factor(6 marks)

### Answer any one question from Q5 and Q6

**5 (a)** Three identical coils, each having resistance of 15Ω and inductance of 0.03 H, are connected in delta across a 3 phase ,400 V,50 Hz supply. Calculate:

(i) the phase current,

(ii) the line current,

(iii) the power consumed(7 marks)
**5 (b)** Derive the expression for line voltage in teRMS of phase
Voltage for three phase star connected balanced load, with phasor diagram across three phase supply.(6 marks)
**6 (a)** An emf given by v=100 sin 100πt is impressed across a circuit consisting of resistance of 40π in series with 100 μF capacitor and 0.25 H inductor. Determine:(i) RMS value of the current, (ii) power consumed, (iii) power factor.(7 marks)
**6 (b)** For a single phase A.C. circuit, the applied voltage is v=V_{m}sin ωt and current drawn is i=I_{m} sin (ωt-ϕ). Derive expression for average power. Draw waveform of voltage, current and instantaneous power over one cycle of voltage.(6 marks)

### Answer any one question from Q7 and Q8

**7 (a)** State and explain Thevenin's Theorem.(6 marks)
**7 (b)** Apply Kirchhoff's Law to calculate current drawn by 4Ω resistance for the circuit.
(7 marks)
**8 (a)** Derive formula to convert DELTA connected network into its STAR connected equivalent circuit.(6 marks)
**8 (b)** Apply superposition theorem to calculate current flowing in 3Ω resistance for the network.
(7 marks)