Power systems miscellaneous Difficult Questions and Answers

Gradient at a distance x,

g =	V
	xIn(R/r)

∴ g_min =	V		, and
	RIn	R

		r

g_max =	V
	rIn	R

		r

and plot of the gradient at the surface of the conductor and the ratio (r/R) is shown in the figure and it can be seen that

r	<	1	< 0.368
R		e

Correct Option: D

Gradient at a distance x,

g =	V
	xIn(R/r)

∴ g_min =	V		, and
	RIn	R

		r

g_max =	V
	rIn	R

		r

and plot of the gradient at the surface of the conductor and the ratio (r/R) is shown in the figure and it can be seen that

r	<	1	< 0.368
R		e

Figure depicts the equivalent circuit for a cable represented by leak age resistance R and capacitance C.
From phasor diagram,
power factor angle, φ = 90° – δ
or cos φ = cos (90° – δ) = sin δ

Correct Option: A

When all the three materials are subjected to the same maximum stress,

g_max =	λ	=	λ	=	λ
	2πε₁r		2πε₂r₁		2πε₃r₂

or ε₁r = ε₂r₁ = ε₃r₂
Since r < r₁ < r₂,
Therefore ε₁ > ε₂ > ε₃
Thus, the dielectric material with highest permittivity should be placed near the conductor and other layer in the descending order.

Correct Option: C

When all the three materials are subjected to the same maximum stress,

g_max =	λ	=	λ	=	λ
	2πε₁r		2πε₂r₁		2πε₃r₂

Let Q'_c be t he reactive power of the shunt capacitor, E_r receiving end voltage, X is the line reactance.
Then voltage drop across it

=		Q_c		. X
		E_r

where, Q_c be the reactive power of the series capacitor, then voltage drop across it

sin φ_v =		Q_c		,
		I

where φ_v is the power factor angle.
For equal voltage boost,

Q'_c	X =	Q_csin φ_v
E_r	X =	I

or	Q'_c	=	sin φ_v	=	0.6	= 6
	Q_c		IX/E_r		0.1

Q'_c > Q_c