A rectangular voltage wave is impressed on a loss-free overhead line, with the far end of the line being short

Question

A rectangular voltage wave is impressed on a loss-free overhead line, with the far end of the line being short-circuited. On reaching the end of this line

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Option A: The current wave is reflected back with positive sign, but the voltage wave with negative sign

Explanation & Concepts:
When a voltage wave reaches a short-circuited end of a loss-free overhead line, the voltage reflection coefficient is -1, causing the total voltage to become zero. Conversely, the current reflection coefficient is +1, causing the reflected current wave to add to the incident wave, doubling the current.

Working Principle: The reflection coefficients for voltage ($\beta_v$) and current ($\beta_i$) are defined by the load impedance ($Z_L$) and surge impedance ($Z_0$). For a short circuit, $Z_L = 0$. Using $\beta_v = \frac{Z_L - Z_0}{Z_L + Z_0}$, we get $\beta_v = -1$. Using $\beta_i = \frac{Z_0 - Z_L}{Z_0 + Z_L}$, we get $\beta_i = +1$.

Key Formulas: $\beta_v = \frac{Z_L - Z_0}{Z_L + Z_0}$ — Voltage reflection coefficient; $\beta_i = \frac{Z_0 - Z_L}{Z_0 + Z_L}$ — Current reflection coefficient

Key Points: For a short-circuited line, $Z_L = 0$ resulting in $\beta_v = -1$ and $\beta_i = +1$.; The reflected voltage wave cancels the incident wave at the short-circuited point to maintain zero voltage.; The reflected current wave reinforces the incident wave, doubling the current at the point of short circuit.

Advantages: Useful for calculating transient current spikes during line-to-ground faults.; Essential for understanding protection relay requirements.

Disadvantages: High current doubling can cause mechanical damage to conductors.; Over-voltage concerns exist if the termination was open-circuited instead.

Applications: Protection system coordination for transmission lines.; Analysis of fault transients in power networks.

Additional Info: Loss-free lines assume $R=0$ and $G=0$.. Option B is wrong because it swaps the signs of the reflection coefficients.

Answer: A is correct — The voltage reflection coefficient at a short circuit is -1 and the current reflection coefficient is +1.

Exam Tip: Remember: Voltage follows the polarity of the impedance mismatch, while current follows the inverse logic for short circuits ($Z_L=0$) vs open circuits ($Z_L=\infty$).

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Option B: The current wave is reflected back with negative sign, but the voltage wave with positive sign

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Option C: Both the current and the voltage waves are reflected with positive sign

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Option D: Both the current and the voltage waves are reflected with negative sign

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