# GATE EE 2004

 Question 1
The value of Z in figure, which is most appropriate to cause parallel resonance at 500 Hz is
 A 125.00 mH B 304.20 $\mu F$ C 2.0 $\mu F$ D 0.05 $\mu F$
Electric Circuits   Resonance and Locus Diagrams
Question 1 Explanation:
Atresonance, the circuit should be in unity power factor.
Hence, 'Z' should be capacitive.
$Y=\frac{1}{jL\omega }+\frac{1}{1/jC\omega }=0$
$\frac{-1}{L\omega }+C\omega =0$
$\therefore \;\; C=\frac{1}{L\omega ^2}=\frac{1}{2(2 \pi \times 500)^2} =0.05\mu F$
 Question 2
A parallel plate capacitor is shown in figure. It is made two square metal plates of 400 mm side. The 14 mm space between the plates is filled with two layers of dielectrics of $\varepsilon _r$= 4, 6 mm thick and $\varepsilon _r$= 2, 8 mm thick. Neglecting fringing of fields at the edge the capacitance is
 A 1298 pF B 944 pF C 354 pF D 257pF
Electromagnetic Fields   Electrostatic Fields
Question 2 Explanation:
When two capacitor formed by two layer of dielectics are connected in series, then equivalent capacitance
\begin{aligned} C_{eq} &= \frac{C_1 \times C_2}{C_1+C_2}\\ &=\frac{\frac{\varepsilon _{r1} \varepsilon _0 A}{d_1} \times \frac{\varepsilon _{r2} \varepsilon _0 A}{d_2}}{\frac{\varepsilon _{r1} \varepsilon _0 A}{d_1} + \frac{\varepsilon _{r2} \varepsilon _0 A}{d_2}} \\ &= \frac{(8.85 \times 10^{-12})(400 \times 10^{-3})^2 \times 4 \times 2}{4 \times 8 \times 10^{-3}+6 \times 2 \times 10^{-3}} \\ & =257 \; \text{pF} \end{aligned}
 Question 3
The inductance of a long solenoid of length 1000 mm wound uniformly with 3000 turns on a cylindrical paper tube of 60 mm diameter is
 A 3.2 $\mu H$ B 3.2 mH C 32.0 mH D 3.2 H
Electromagnetic Fields   Magnetostatic Fields
Question 3 Explanation:
Let, $B=\mu _0nI$
Then, $\phi =B.S=\mu _0nSI$
Where 'S' is the cross sectional area of solenoid flux linkage,
$a'=n\phi =\mu _0n^2SI$
Hence, Inductance length $=\mu _0n^2S$
For,
$l=1000mm=1m$
$\therefore \;\;L=4 \pi \times 10^{-7} \times 3000^2 \times \pi \times (30 \times 10^{-3})^2$
$\;\;\;=32mH$
 Question 4
Total instantaneous power supplied by a 3-phase ac supply to a balanced R-L load is
 A zero B constant C pulsating with zero average D pulsating with the non-zero average
Power Systems   Power System Transients
Question 4 Explanation:
$=Z_L=R+j\omega L=|Z|\angle \theta _L$
where, $\theta _L=\tan ^{-1}\left ( \frac{\omega L}{R} \right )$
Voltages of $3-\phi$ supply
\begin{aligned} V_a&=V_m \sin \omega t \\ V_b&=V_m \sin (\omega t-120^{\circ}) \\ V_c &=V_m \sin (\omega t+120^{\circ}) \\ I_a&=\frac{V_a}{Z_L}=\frac{V_m \sin \omega t}{|Z|\angle \theta _L} \\ &= I_M \sin (\omega t-\theta _L)\\ \text{where, } I_m&=\frac{V_m}{|Z|}\\ \text{Similarly,}&\\ I_b&=I_m \sin (\omega t-120-\theta _L)\\ I_c&=I_m \sin (\omega t+120-\theta _L)\\ & \text{Instantaneous power}\\ &=P=V_aI_a+V_bI_b+V_cI_c\\ P&=V_mI_m[\sin \omega t\cdot \sin (\omega t-\theta _L)\\ &+\sin (\omega t-120^{\circ}) \cdot \sin (\omega t-120-\theta _L)\\ &+\sin (\omega t+120^{\circ})\cdot \sin (\omega t+120-\theta _L)]\\ &=\frac{V_mI_m}{2}[(\cos \theta _L -\cos(2\omega t-\theta _L) ) \\ &+(\cos \theta _L -\cos(2\omega t-240-\theta _L) )\\ &+(\cos \theta _L -\cos(2\omega t+240-\theta _L) )]\\ P&=\frac{3V_mI_m}{2}\cos \phi = \text{constant} \end{aligned}
 Question 5
A 500 kVA, 3-phase transformer has iron losses of 300 W and full load copper losses of 600 W. The percentage load at which the transformer is expected to have maximum efficiency is
 A 50.00% B 70.70% C 141.40% D 200.00%
Electrical Machines   Transformers
Question 5 Explanation:
\begin{aligned} P_{cu} &=x^2 \times [\text{Full load copper loss}] \\ &= x^2 \times P_{fl,cu}\\ \text{where,}\;\; x&= \text{fraction of laod} \end{aligned}
Maximum occurs when
Copper loss-Iron loss
$x^2 \times P_{fl,cu}=P_i$
$x^2 \times 600=300 x=0.707 =70.7\%$
 Question 6
For a given stepper motor, the following torque has the highest numerical value
 A Detent torque B Pull-in torque C Pull-out torque D Holding torque
Electrical Machines   Single Phase Induction Motors, Special Purpose Machines and Electromechanical Energy Conversion System
Question 6 Explanation:
Detent torque: It is amount of torque that the motor produces when it is not energized. No current is slowing through the winding.
Holding Torque: It is amount of torque that the motor produces when it has rated current flowing through the winding but motor is at rest..
Pull-in Torque: Shows the maximum value of torque at given speeds that the motor can start, stop, or reverse in synchronism with the input pulses.
Pull-out Torque: Shows the maximum value of torque at given speeds that the motor can generate while running in synchronism. If the motor is run outside of this curve, it will stall.
 Question 7
The following motor definitely has a permanent magnet rotor
 A DC commutator motor B Brushless dc motor C Stepper motor D Reluctance motor
Electrical Machines   Single Phase Induction Motors, Special Purpose Machines and Electromechanical Energy Conversion System
Question 7 Explanation:
Brushless dc motor definitely has a permanent magnet.
 Question 8
The type of single-phase induction motor having the highest power factor at full load is
 A shaded pole type B split-phase type C capacitor-start type D capacitor-run type
Electrical Machines   Single Phase Induction Motors, Special Purpose Machines and Electromechanical Energy Conversion System
Question 8 Explanation:
Capacitor start type motor has high staring torque and therefore is used for hard starting loads such as compressor, conveyors, pumps et.
Capacitor-run type motor has better running power factor and efficiency and a quiter and smoother operation. It is used for both easy and hard to start loads. Moder applications of such motors are ceiling fans, blower etc.
 Question 9
The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage having phase sequence A-B-C. For counter clockwise rotation of the motor, the phase sequence of the power supply should be
 A B-C-A B C-A-B C A-C-B D B-C-A or C-A-B
Electrical Machines   Three Phase Induction Machines
Question 9 Explanation:
To reverse the direction of rotation, phase sequence of the supply has to be reversed. For clockwise direction, the phase sequence was A-B-C. For counter-clockwise direction, the phase sequence has to be A-C-B.
 Question 10
For a linear electromagnetic circuit, the following statement is true
 A Field energy is equal to the co-energy B Field energy is greater than the co-energy C Field energy is lesser than the co-energy D Co-energy is zero
Electrical Machines   Single Phase Induction Motors, Special Purpose Machines and Electromechanical Energy Conversion System
Question 10 Explanation:

Where, $\lambda =N\phi =$Flux linkage
Field energy is the energy absorbed by the magnetic system to establish flux $\phi$.
For a linear electromagnetic circuit
Field energy = Co-energy $=\frac{1}{2}\lambda i$
There are 10 questions to complete.