## Basic Electrical Engineering (BEE) - Dec 2015

### First Year Engg (Semester 1)

TOTAL MARKS:

TOTAL TIME: HOURS

### Solve any one question from Q1 and Q2

**1 (a)** Obtain the equation for coefficient of coupling between two coils placed on common magnetic field.(6 marks)
**1 (b)** A water pump lifts 50 m^{3} of water per hour to a height of 20 m. The overall efficiency of water pump set is 0.60. Find monthly bill, when the pump is used 4 hours a day for a month of 30 days, at the rate of Rs. 5/kWh.(6 marks)
**2 (a)** Explain the effect of temperature on resistance of:

(i) metal conductors

(ii) insulators

(iii) alloys.(6 marks)
**2 (b)** A steel ring of mean diameter of 50 cm is wound with
500 turns on it. A flux density of 1 Tesla is produced in
the ring by mmf of 4000 AT/m. Calculate magnetising current. Also find the current when an air gap of 1 mm is cut in it, keeping B = 1 Tesla in the ring.(6 marks)

### Solve any one question from Q3 and Q4

**3 (a)** Obtain the expression for composite capacitor having 3-dielectric materials.(7 marks)
**3 (b)** A 50 Hz sinusoidal voltage has rms value of 200 V. At
t = 0, the instantaneous value is positive and half of its maximum value. Write down the expression for voltage and sketch the wave form.(6 marks)
**4 (a)** Derive an equation for average value of sinusoidal current in terms of its peak value.(6 marks)
**4 (b)** A 40 kVA, 2200/220 V, 50 Hz, 1-ph transformer has an iron loss of 250 W. The resistances of low and high voltage windings are 0.005 Ω and 0.5 Ω respectively. Calculate efficiency at full load and load p.f. = 0.8 lagging.(7 marks)

### Solve any one question from Q5 and Q6

**5 (a)** Obtain the expression for power, if x = v_{m} sin out is applied to R-L series circuit.(6 marks)
**5 (b)** Three identical impedances each of 6 + j8 Ω are connected
in star across 3-ph, 400 V, 50 Hz a.c. supply. Calculate:

(i) line current

(ii) active power

(iii) reactive power.(7 marks)
**6 (a)** What is series resonance? Obtain the equation for resonant frequency.(6 marks)
**6 (b)** Two circuits having impedances Z_{1} = 8 + j6 Ω and Z_{2} = 5 +j10 Ω are connected in parallel across 200 V, 50 Hz, 1-ph a.c. supply. Calculate:

(i) current drawn by each circuit

(ii) total current

(iii) p.f. of whole circuit.(7 marks)

### Solve any one question from Q7 and Q8

**7 (a)** Using simple series-parallel combination, find R_{BC} for Fig 1.
(6 marks)
**7 (b)** Obtain the equations to convert A-connected resistances into equivalent star circuit.(6 marks)
**8 (a)** State the Thevenin's theorem and explain the steps to find R_{th}, V_{th} and I_{th}.(6 marks)
**8 (b)** Using Mesh/Loop analysis, calculate current flowing through R_{BC} for Fig 2.
(6 marks)