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A transmission line of 200 Km is supplying at 50Hz frequency. What is the percentage rise in voltage at reciving end?
  • a)
    20%
  • b)
    1.2%
  • c)
    2.19%
  • d)
    20.8%
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A transmission line of 200 Km is supplying at 50Hz frequency. What is ...
To calculate the percentage rise in voltage at the receiving end of a transmission line, we need to consider the line length, frequency, and the characteristics of the transmission line itself.

Given:
- Transmission line length: 200 km
- Frequency: 50 Hz

The percentage rise in voltage can be calculated using the equation:

Percentage rise in voltage = (2 * π * frequency * line length * Zc) / (√3 * Vr)

Where:
- π = Pi (approximately equal to 3.14)
- frequency = 50 Hz
- line length = 200 km (or 200,000 m)
- Zc = characteristic impedance of the transmission line
- Vr = receiving end voltage

Let's break down the calculation into steps:

1. Calculate the wavelength (λ) of the transmission line:
Wavelength (λ) = (speed of light) / frequency
The speed of light is approximately 3 x 10^8 m/s.
So, λ = (3 x 10^8 m/s) / (50 Hz) = 6 x 10^6 m

2. Calculate the characteristic impedance (Zc) of the transmission line:
Zc = √(L/C)
Where L is the inductance per unit length and C is the capacitance per unit length of the transmission line.
For a long transmission line, L/C = (R/G), where R is the resistance per unit length and G is the conductance per unit length.
Assuming the transmission line is lossless, R = 0 and G = 0.
Therefore, Zc = √(0/0) = undefined

3. Since the characteristic impedance (Zc) is undefined, we need to consider the surge impedance (Zs) of the transmission line, which is given by:
Zs = √(L/C)
For a long transmission line, Zs = √(R/G)
Again assuming the transmission line is lossless, Zs = √(0/0) = undefined

4. Calculate the percentage rise in voltage using the surge impedance (Zs):
Percentage rise in voltage = (2 * π * frequency * line length * Zs) / (√3 * Vr)
Since Zs is undefined, we cannot calculate the percentage rise in voltage using this equation.

Based on the given information, it appears that the calculation of the percentage rise in voltage is not possible without additional data. The correct answer cannot be determined using the given parameters.
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Community Answer
A transmission line of 200 Km is supplying at 50Hz frequency. What is ...
Percentage rise in voltage = (ω2 l2 10-8)/18
Solving this % Vrise = {(2 × Ω × 50) × 2002 × 10-8}/18
= 2.19%.
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