GATE EE 2007

 Question 1
The common emitter forward current gain of the transistor shown is $\beta _{F}=100$.

The transistor is operating in
 A Saturation region B Cutoff region C Reverse active region D Forward active region
Analog Electronics   BJT, FET and their Biasing Circuits
Question 1 Explanation:
We assume BJT is in active region, applying KVL in base emitter circuit

$10-0.7=1k\Omega \times I_c+270 \times I_b$
$=I_b(270+100k)$
$\therefore \; \; I_b=\frac{9.3}{370}mA$
$\therefore \;\; I_c=\frac{93}{37}mA$
$I_{c(sat)}=\frac{10-0.2}{2k}=4.9 mA$
$I_{c(sat)} \gt I_{c(active)}$
$\therefore \;$ BJT is in active region.
 Question 2
The three-terminal linear voltage regulator is connected to a 10 $\Omega$ load resistor as shown in the figure. If $V_{in}$ is 10 V, what is the power dissipated in the transistor ?
 A 0.6W B 2.4W C 4.2W D 5.4W
Analog Electronics   Diodes and their Applications
Question 2 Explanation:

$V_0=V_Z-V_{BE}$
$\;\; =6.6V-0.7V=5.9V$
$I_L=\frac{V_0}{R_L}=\frac{5.9}{10}=0.59A=I_C$
$V_{CE}-V_i-V_0$
$\;\; =10-5.9=4.1V$
$P_Q=V_{CE} \times I_C$
$\;\;=4.1 \times 0.59A=2.4 W$

 Question 3
Consider the transformer connections in a part of a power system shown in the figure. The nature of transformer connections and phase shifts are indicated for all but one transformer.

Which of the following connections, and the corresponding phase shift $\theta$, should be used for the transformer between A and B ?
 A Star-Star ($\theta=0^{\circ}$) B Star-Delta ($\theta=-30^{\circ}$ ) C Delta-Star ($\theta=30^{\circ}$) D Star-Zigzag ($\theta=30^{\circ}$)
Power Systems   Switch Gear and Protection
Question 3 Explanation:

Taking $V_1$ as the reference
$V_1=220\angle 0^{\circ}kV$
$\angle \theta _1=0^{\circ}$
Phase difference $V_2$ and $V_1$ is $0^{\circ}$.
So, $V_2=400\angle 0^{\circ}kV$
$V_2$ leads $V_3$ by $30^{\circ}$.
So, $V_3=15\angle -30^{\circ}kV$
$\angle \theta _3=-30^{\circ}$
$V_3$ lags $V_4$ by $30^{\circ}$.
$\angle \theta _3=\angle \theta _4-30^{\circ}$
$\angle \theta _4=\angle \theta _3+30^{\circ}$
$\angle \theta _4=-30^{\circ}+30^{\circ}=0^{\circ}$
Phase difference between $V_1$ and $V_2$ is $\theta$
$\theta =\angle \theta _1-\angle \theta _4=0-0=0^{\circ}$
 Question 4
The incremental cost curves in Rs/MWhr for two generators supplying a common load of 700 MW are shown in the figures. The maximum and minimum generation limits are also indicated. The optimum generation schedule is :
 A Generator A : 400 MW, Generator B : 300 MW B Generator A : 350 MW, Generator B : 350 MW C Generator A : 450 MW, Generator B : 250 MW D Generator A : 425 MW, Generator B : 275 MW
Power Systems   Economic Power Generation and Load Dispatch
Question 4 Explanation:
Maximum incremental cost in Rs/Mwhr for generator A =600 (at 450 MW)
Minimum incremental cost in Rs/Mwhr for generator B =650 (at 150 MW)
As maximum value of incremental cost of A is less than minimum value of B.
Therefore, generator 'A' will operate at its maximum (o/p) 450 MW and B at (700-450)=250 MW.
 Question 5
Two regional systems, each having several synchronous generators and loads are inter connected by an ac line and a HVDC link as shown in the figure. Which of the following statements is true in the steady state :
 A Both regions need not have the same frequency B The total power flow between the regions ($P_{ac}+P_{dc}$) can be changed by controlled the HDVC converters alone C The power sharing between the ac line and the HVDC link can be changed by controlling the HDVC converters alone. D The directions of power flow in the HVDC link ($P_{dc}$) cannot be reversed
Power Systems   High Voltage DC Transmission
Question 5 Explanation:
Both region are connected by HVDC link as well as AC line. So AC link is possible when both regions have frequency.
By changing fringe angle ($\alpha$) of converter, we can change the power sharing, between the AC line and HVDC link.

There are 5 questions to complete.