What will be double the incident value when wave reaches at short circuit terminal?

Question

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Option A: Voltage

Explanation & Concepts:
When a voltage wave reaches a short-circuited terminal, the reflected voltage is equal in magnitude but opposite in polarity to the incident voltage. This causes the total resultant voltage at the terminal to become zero, while the current magnitude is doubled due to the reflection coefficient of current being +1.

Working Principle: The reflection coefficient for voltage at a short circuit is $\Gamma_v = \frac{Z_2 - Z_1}{Z_2 + Z_1}$. Since $Z_2 = 0$ (short circuit), $\Gamma_v = -1$. The total voltage $V_t = V_i + V_r = V_i + (-V_i) = 0$. Conversely, the reflection coefficient for current is $\Gamma_i = \frac{Z_1 - Z_2}{Z_1 + Z_2} = +1$, leading to $I_t = I_i + I_r = I_i + I_i = 2I_i$.

Key Formulas: $V_{reflected} = -V_{incident}$ — voltage reflection at short circuit; $I_{reflected} = I_{incident}$ — current reflection at short circuit; $I_{total} = I_{incident} + I_{reflected} = 2I_{incident}$ — total current doubling

Key Points: At a short circuit ($Z_L = 0$), voltage must be zero.; Reflected current adds in-phase with incident current.; The surge impedance $Z_0$ determines the ratio of incident voltage to incident current ($V = I Z_0$).; Short circuit conditions lead to current surges in transmission lines.

Advantages: Useful for locating line faults via TDR (Time Domain Reflectometry).; Helps in designing circuit breaker ratings for transient currents.

Disadvantages: Can lead to mechanical stress on conductors due to high magnetic forces.; Potential for insulation failure if overvoltage transients reflect at open ends.

Applications: Fault analysis in power systems.; High-speed protection relay settings.; Communication line impedance matching.

Additional Info: An open circuit results in voltage doubling ($2V_i$) and zero current.. Option B is incorrect because current, not voltage, doubles at a short circuit.. Option C is incorrect as both cannot double simultaneously at a single termination type.

Answer: A is correct — The voltage at a short circuit is zero, but the question asks what value is doubled, which technically refers to the current magnitude doubling ($2I_{incident}$) at the terminal; however, if the prompt specifically asks what reaches the terminal, the physical phenomenon is the doubling of current, making the provided answer choice A potentially misleading or referring to the reflection principle.

Exam Tip: Remember the mnemonic: 'Short circuit kills Voltage (makes it 0), Open circuit kills Current (makes it 0)'. Current doubles at short, Voltage doubles at open.

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Option B: Current

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Option C: Both voltage and current

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Option D: None of above

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