1
GATE EE 2018
+1
-0.33
In the figure, the voltages are

$${v_1}\left( t \right) = 100\cos \left( {\omega t} \right)$$

$${v_2}\left( t \right) = 100\cos \left( {\omega t + {\pi \over {18}}} \right)$$

and $${v_3}\left( t \right) = 100\cos \left( {\omega t + {\pi \over {36}}} \right)$$.

The circuit is in sinusoidal steady state, and R << $${\omega L}$$. P1, P2 and P3 are the average power outputs. Which one of the following statements is true?
A
P1 = P2 = P3 = 0
B
P1 < 0, P2 > 0, P3 > 0
C
P1 < 0, P2 > 0, P3 < 0
D
P1 > 0, P2 < 0, P3 > 0
2
GATE EE 2017 Set 2
Numerical
+1
-0
The normal - $$\pi$$ circuit of a transmission line is shown in the figure.

Impedance $$Z = 100\angle {80^ \circ }$$ and reactance $$\,X = 3300\Omega .$$ The magnitude of the characteristic impedance of the transmission line, in $$\Omega ,$$ is ________. (Give the answer up to one decimal place.)

3
GATE EE 2017 Set 1
+1
-0.3
A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $$v_{an}=220\sin\left(100\mathrm{πt}\right)\;V$$ and $$i_a=10\sin\left(100\mathrm{πt}\right)\;A$$, respectively. Similarly for phase-b the instantaneous voltage and current are $$v_{bn}=220\cos\left(100\mathrm{πt}\right)\;V$$ and $$i_b=10\cos\left(100\mathrm{πt}\right)\;A$$, respectively. The total instantaneous power flowing form the source to the load is
A
2200 W
B
$$2200\;\sin^2\left(100\mathrm{πt}\right)\;W$$
C
4400 W
D
$$2200\;\sin\left(100\mathrm{πt}\right)\cos\left(100\mathrm{πt}\right)\;W$$
4
GATE EE 2014 Set 3
+1
-0.3
In a long transmission line with $$r, l, g$$ and $$𝑐$$ are the resistance, inductance, shunt conductance and capacitance per unit length respectively, the condition for distortionless transmission is
A
$$rc = \ell g$$
B
$$r = \ell /r$$
C
$$rg = \ell c$$
D
$$g = \sqrt {c/\ell }$$
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