1
GATE EE 2015 Set 2
Numerical
+2
-0
A composite conductor consists of three conductors of radius $$R$$ each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is ______.
2
GATE EE 2015 Set 2
+2
-0.6
The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t1 by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle $$\delta$$ shows the transient correctly?
A
B
C
D
3
GATE EE 2015 Set 2
Numerical
+2
-0
The incremental costs (in rupees/$$MWh$$) of operating two generating units are functions of their respective powers $${P_1}$$ and $${P_2}$$ in $$MW,$$ and are given by $${{d{C_1}} \over {d{P_1}}} = 0.2{P_1} + 50$$$$${{d{C_2}} \over {d{P_2}}} = 0.24{P_2} + 40$$$
Where, \eqalign{ & 20\,MW \le {P_1} \le 150\,MW \cr & 20\,MW \le {P_2} \le 150MW. \cr}\$
For a certain load demand, $${P_1}$$ and $${P_2}$$ have been chosen such that $$\,\,d{C_1}/d{P_1} = 76\,Rs/MWh\,\,$$ and $$\,d{C_2}/d{P_2} = 68.8\,Rs/MWh.\,\,$$ If the generations are rescheduled to minimize the total cost, then $${P_2}$$ is ____________.
4
GATE EE 2015 Set 2
+2
-0.6
A $$3$$-phase transformer rated for $$33 kV/11kV$$ is connected in delta/star as shown in figure. The current transformers $$\left( {C{T_s}} \right)$$ on low and high voltage sides have a ratio of $$500/5.$$ Find the currents $${i_1}$$ and $${i_2}$$, if the fault current is $$300$$ $$A$$ as shown in figure.
A
$${i_1} = {1 \over {\sqrt 3 }}A,\,\,{i_2} = 0\,A$$
B
$${i_1} = 0\,A,\,\,{i_2} = 0\,A$$
C
$${i_1} = 0\,A,\,\,{i_2} = {1 \over {\sqrt 3 }}A$$
D
$${i_1} = {1 \over {\sqrt 3 }}A,\,\,{i_2} = {1 \over {\sqrt 3 }}A$$
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