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

Question

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Option A: Voltage

Explanation & Concepts:
When a traveling voltage wave hits an open-circuit terminal, the reflected voltage wave is equal in magnitude and polarity to the incident wave, resulting in a total voltage at the terminal equal to double the incident value. This happens because the boundary condition at an open circuit requires the total current to be zero.

Working Principle: According to the transmission line theory, the reflection coefficient for voltage is $ho_v = \frac{Z_L - Z_0}{Z_L + Z_0}$. For an open circuit, the load impedance $Z_L 	o \infty$, which makes $ho_v = 1$. The total voltage at the load is $V_L = V_i + V_r = V_i(1 + ho_v) = 2V_i$.

Key Formulas: $V_{reflected} = ho_v \cdot V_{incident}$ — Relation for reflected voltage wave; $ho_v = \frac{Z_L - Z_0}{Z_L + Z_0}$ — Voltage reflection coefficient

Key Points: At an open circuit, current reflection coefficient $ho_i = -1$.; The total current at the open terminal is $I_L = I_i + I_r = I_i(1 - 1) = 0$.; The voltage doubles at the terminal due to the superposition of incident and reflected waves.; This phenomenon is a critical consideration in insulation coordination.

Advantages: Provides a simple model for analyzing transients in power systems; Allows for calculation of surge voltage stress on equipment

Disadvantages: Does not account for line losses or frequency-dependent parameters; Assumes an ideal lossless line

Applications: Protection of transformers against lightning surges; Design of surge arresters in high voltage substations

Additional Info: For a short circuit termination, the voltage reflection coefficient is -1, causing the total voltage to become zero.. Option B is incorrect because current must be zero at an open circuit terminal.

Answer: A is correct — The total voltage at an open-circuit terminal is the sum of incident and reflected voltage waves, which equals twice the incident voltage.

Exam Tip: Remember that voltage doubles at an open end, while current doubles at a short-circuited end during transient propagation.

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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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