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 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

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.)

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