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Test: Calculation of Inductance of Transmission Line - Electrical Engineering (EE) MCQ


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10 Questions MCQ Test - Test: Calculation of Inductance of Transmission Line

Test: Calculation of Inductance of Transmission Line for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Test: Calculation of Inductance of Transmission Line questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Calculation of Inductance of Transmission Line MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Calculation of Inductance of Transmission Line below.
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Test: Calculation of Inductance of Transmission Line - Question 1

The geometric mean radius of a conductor, having four equal strands with each strand of radius ‘r’, as shown in the figure below, is

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 1

Concept:
GMR is defined as the effective distance over which self magnetic flux linkages occur
For a solid conductor with radius r,

GMR = r' = 0.7788r
GMR is less than the physical radius of the conductor.
In the given figure, standard conductor with four identical strands touching each other is given with equal radius r.


= 1.722 r
Since each strands are identical.
∴ GMR of conductor will be equal to GMR of strand i.e.,
GMRcond = GMRa1
= 1.722 r
Therefore, correct option is (d)

Test: Calculation of Inductance of Transmission Line - Question 2

(I) Unsymmetrical spacing configurations cause the line interference.
(II) Unsymmetrical spacing causes the voltage induction in the communication lines.
The above problems can be eliminated by ________ 

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 2

Effect of Unsymmetrical Spacing of 3ϕ Line Conductors:

  1. Due to unsymmetrical spacing, flux linkage with all three phases is different. Because of this, there will be an unequal voltage drop in all three phases. Thus the voltage at the receiving end will not be the same for the three phases. 
  2. Due to unsymmetrical spacing, the magnetic field external to the conductor is not zero. Thereby causing the induced voltage in adjacent electric circuits, thus producing the interference in communication lines.
  3. Unsymmetrical spacing configurations cause line interference.

​The above-mentioned problems can be eliminated by the transposition of the 3ϕ line.

Transposition is the periodic swapping of positions of the conductors of a transmission line, in order to reduce interference and voltage induction in the 3ϕ transmission line.

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Test: Calculation of Inductance of Transmission Line - Question 3

The inductance of a power transmission line increases with

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 3

The inductance of a transmission line is given by,

Where, d = distance between the conductors
r’ = 0.7788r
r = radius of conductors
Therefore, if we increase the spacing between the phase conductors, the value of line inductance will increase.

Test: Calculation of Inductance of Transmission Line - Question 4

If the height of transmission tower is increased:

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 4

Concept:

  • The inductance of a transmission line is independent of the height of the transmission tower.
  • The capacitance of the transmission line is dependent on the height of the transmission tower.
  • If tower height increases then the distance between the current carrying wire and ground increases, and line-to-ground capacitance decreases, as capacitance is inversely proportional to the distance between the line and earth.
  • While there is no effect on line to line capacitance.
Test: Calculation of Inductance of Transmission Line - Question 5

Refer to the following figure; the radius of each conductor is 0.03 m. It is also known that the spacing between phase conductors is 35 cm and the distance between the phases (D) is 4 m. Find the value of the average inductance of three-phase line arranged.

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 5

Calculation:
Self GMD or GMR:

  • Self GMD is also called GMR. GMR stands for Geometrical Mean Radius. 
  • GMR is calculated for each phase separately.
  • self-GMD of a conductor depends upon the size and shape of the conductor
  • GMR is independent of the spacing between the conductors.

GMD:

  • GMD stands for Geometrical Mean Distance.
  • It is the equivalent distance between conductors.
  • GMD depends only upon the spacing 
  • GMD comes into the picture when there are two or more conductors per phase.​

The inductance per phase is given as,

GMD = Mutual Geometric Mean Distance = D
GMR = 0.7788r
r = Radius of the conductor​
Calculation:
Given conductor configuration,

r = 0.03 m
d = 35 cm = 0.35 m
D = 4 m

The inductance per phase is given as,

L = 0.8041 mH/km
Note: According to the Official UPRVUNL JE EE 2014 Previous Year Paper, then select option was 2.2 mH/km. Because of calculation, We correct the option accordingly

Test: Calculation of Inductance of Transmission Line - Question 6

A three-phase line has its conductors at the corners of an equilateral triangle of side 1 m. The radius of each conductor is (1/0.7788) cm. The inductance per phase per km is given by:

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 6

Concept:
The inductance of a three-phase line having its conductors at the corners of an equilateral triangle is given by:

Calculation:
Given, a = 1m

L = 9.21 H/m
L = 9.21 × 10-1 mH\km
L = 0.921 mH\km

Test: Calculation of Inductance of Transmission Line - Question 7

A single-phase transmission line consists of two parallel conductors one meter apart and 1.25 cm in diameter. The loop inductance per km of the line is:

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 7

Concept:
The inductance of a transmission line consists of two parallel conductors is given by,

Where, d = distance between the conductors
r’ = 0.7788 r
r = radius of conductors
Calculation:
Given
d = 1 m
Diameter (D) = 1.25 cm
r = 0.625 cm = 0.625 × 10-2 m
r' = 0.7788 r

L = 21.3 × 10-4 Henry/ km

*Answer can only contain numeric values
Test: Calculation of Inductance of Transmission Line - Question 8

Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab = Dbc = Dca = 1 m as shown in figure below. The resistances of the conductors are neglected. The geometric mean radius (GMR) of each conductor is 0.01 m. Neglecting the effect of ground, the magnitude of positive sequence reactance in Ω/km (rounded off to three decimal places) is _________


Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 8


Dab = Dbc = Dca = 1m
GMD = 1 m
GMR = 0.01 m
frequency (f) = 50 Hz

= 9.21 × 10-7 H/m
XL = 2πfL
= 2π × 50 × 9.21 × 10-7
= 0.2893 × 10-3 Ω/m
= 0.2893 Ω/km

*Answer can only contain numeric values
Test: Calculation of Inductance of Transmission Line - Question 9

A single-phase transmission line has two conductors each of 10mm radius. These are fixed at a center-to-center distance of 1m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three-phase system is to be 5% more than that of the inductance per conductor of the single-phase system. The distance D, in meters, is _______.


Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 9

When single phase,


 
When converted to three phase,

Solving , we get

Test: Calculation of Inductance of Transmission Line - Question 10

Directions: It consists of two statements, one labeled as the ‘Statement (I)’ and the other as ‘Statement (II)’. Examine these two statements carefully and select the answer using the codes given below:
Statement (I): The expression for the value of inductance L per conductor of an unsymmetrically spaced 3-phase overhead transmission line contains an imaginary term.
Statement (II): The presence of the imaginary term is due to the mutual inductance between the phase conductors and can be eliminated by symmetrically transposing the three line-conductors along the length of the line.

Detailed Solution for Test: Calculation of Inductance of Transmission Line - Question 10

Consider a 3-ɸ line with conductors A, B, and C; each of radius r metres. Let the spacing between them be d1, d2 and d3 and the current flowing through them be IA, IB and IC respectively.
The inductances for the above arrangements are given by,

Thus we see that when the conductors of a 3-phase transmission line are not equidistant from each other, i.e., unsymmetrically spaced, the flux linkages and inductances of various phases are different which cause unequal voltage drops in the three phases and transfer of power between phases (represented by imaginary terms of the expression for inductances) due to mutual inductances even if the currents in the conductors are balanced.

The unbalancing effect on account of irregular spac­ing of conductors is avoided by the transposition of conduc­tors, as shown in the figure.

The effect of transposition is that each conduc­tor has the same average inductance, which is given as:

Therefore, Statement (I) and Statement (II) are individually true and statement (II) is the correct explanation of statement (II)

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