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A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF is operating at 50 Hz, 400 kV. If this line is terminated with 5 Ω, the voltage across the load as ______ kV.
- a)170
- b)200
- c)370
- d)400
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF...
Zc = 
= 
= 5Ω
Zc = ZL
Hence, VL = VS = 400 kV
Most Upvoted Answer
A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF...
Given data:
Resistance (R) = 6 Ω
Conductance (G) = 240 mS = 0.24 S
Inductance (L) = 2 H
Capacitance (C) = 80 mF = 0.08 F
Operating frequency (f) = 50 Hz
Voltage (V) = 400 kV
Termination resistance (Rt) = 5 Ω
To find: Voltage across the load (Vload) in kV
First, we need to calculate the characteristic impedance (Zc) of the transmission line using the formula:
Zc = sqrt((R + jωL) / (G + jωC))
where ω is the angular frequency, given by ω = 2πf.
Calculating ω:
ω = 2πf = 2π(50) = 100π rad/s
Substituting the given values:
Zc = sqrt((6 + j(100π)(2)) / (0.24 + j(100π)(0.08)))
To simplify the calculation, let's divide the numerator and denominator by 2:
Zc = sqrt((3 + j(100π)(1)) / (0.12 + j(100π)(0.04)))
Now, simplifying the expression inside the square root:
Zc = sqrt((3 + 100jπ) / (0.12 + 4jπ))
To find the magnitude of Zc, we need to find the real and imaginary parts separately:
Real part = 3 / (0.12 + 4jπ) = 3(0.12 - 4jπ) / ((0.12)^2 + (4π)^2)
Imaginary part = 100π / (0.12 + 4jπ) = 100π(0.12 + 4jπ) / ((0.12)^2 + (4π)^2)
Now, calculating the magnitude of Zc:
|Zc| = sqrt((Real part)^2 + (Imaginary part)^2)
Once we have Zc, we can calculate the voltage across the load (Vload) using the voltage division rule:
Vload = V * (Rt / (Rt + Zc))
Substituting the given values:
Vload = (400 kV) * (5 Ω / (5 Ω + Zc))
Calculating Zc and Vload will yield the final answer.
Resistance (R) = 6 Ω
Conductance (G) = 240 mS = 0.24 S
Inductance (L) = 2 H
Capacitance (C) = 80 mF = 0.08 F
Operating frequency (f) = 50 Hz
Voltage (V) = 400 kV
Termination resistance (Rt) = 5 Ω
To find: Voltage across the load (Vload) in kV
First, we need to calculate the characteristic impedance (Zc) of the transmission line using the formula:
Zc = sqrt((R + jωL) / (G + jωC))
where ω is the angular frequency, given by ω = 2πf.
Calculating ω:
ω = 2πf = 2π(50) = 100π rad/s
Substituting the given values:
Zc = sqrt((6 + j(100π)(2)) / (0.24 + j(100π)(0.08)))
To simplify the calculation, let's divide the numerator and denominator by 2:
Zc = sqrt((3 + j(100π)(1)) / (0.12 + j(100π)(0.04)))
Now, simplifying the expression inside the square root:
Zc = sqrt((3 + 100jπ) / (0.12 + 4jπ))
To find the magnitude of Zc, we need to find the real and imaginary parts separately:
Real part = 3 / (0.12 + 4jπ) = 3(0.12 - 4jπ) / ((0.12)^2 + (4π)^2)
Imaginary part = 100π / (0.12 + 4jπ) = 100π(0.12 + 4jπ) / ((0.12)^2 + (4π)^2)
Now, calculating the magnitude of Zc:
|Zc| = sqrt((Real part)^2 + (Imaginary part)^2)
Once we have Zc, we can calculate the voltage across the load (Vload) using the voltage division rule:
Vload = V * (Rt / (Rt + Zc))
Substituting the given values:
Vload = (400 kV) * (5 Ω / (5 Ω + Zc))
Calculating Zc and Vload will yield the final answer.
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A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF is operating at 50 Hz, 400 kV. If this line is terminated with 5 Ω, the voltage across the load as ______ kV.a)170b)200c)370d)400Correct answer is option 'D'. Can you explain this answer?
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A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF is operating at 50 Hz, 400 kV. If this line is terminated with 5 Ω, the voltage across the load as ______ kV.a)170b)200c)370d)400Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF is operating at 50 Hz, 400 kV. If this line is terminated with 5 Ω, the voltage across the load as ______ kV.a)170b)200c)370d)400Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long transmission line has R = 6 Ω, G = 240 mS L = 2 H and C = 80 mF is operating at 50 Hz, 400 kV. If this line is terminated with 5 Ω, the voltage across the load as ______ kV.a)170b)200c)370d)400Correct answer is option 'D'. Can you explain this answer?.
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