For an open circuited line, the resulting current will be

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The correct answer is Option A: Zero. For an ideal open-circuited transmission line, the boundary condition at the receiving end requires that the total current must be zero. This is because there is no path for the charge carriers to flow, resulting in a complete reflection of the incident current wave.

Step-by-Step Solution & Concepts:
For an ideal open-circuited transmission line, the boundary condition at the receiving end requires that the total current must be zero. This is because there is no path for the charge carriers to flow, resulting in a complete reflection of the incident current wave.

Working Principle: When a current wave traveling along a transmission line hits an open circuit, it encounters infinite impedance. To satisfy the boundary condition of zero current, the reflected current wave must be equal in magnitude but opposite in phase to the incident current wave. Mathematically, $I_{total} = I_{incident} + I_{reflected} = 0$, leading to $I_{reflected} = -I_{incident}$.

Key Formulas: $I_{total} = I_{i} + I_{r} = 0$ — Current boundary condition at open circuit; $V_{total} = V_{i} + V_{r} = 2V_{i}$ — Voltage at open circuit (doubling effect)

Key Points: At an open circuit, the impedance is infinite ($Z_L = \infty$).; Current reflection coefficient $\Gamma_i = \frac{Z_0 - Z_L}{Z_0 + Z_L} = -1$.; Voltage reflection coefficient $\Gamma_v = \frac{Z_L - Z_0}{Z_L + Z_0} = +1$.

Advantages: Useful for testing line discontinuities; Essential concept for understanding surge protection

Disadvantages: Can lead to voltage doubling which stresses insulation; Causes standing waves on the line

Applications: Fault analysis in power systems; Transmission line communication signal integrity

Additional Info: The voltage at an open-circuited end is twice the incident voltage, which is why open-circuit conditions are dangerous for insulation.. Option B is incorrect because current cannot be infinite in a physical line; it is zero due to the lack of a return path.

Answer: A is correct — The total current at the open-circuited end of a line is zero because the reflected current perfectly cancels the incident current.

Exam Tip: Always remember that in transient analysis, current 'reflects' with a sign inversion at open circuits, while voltage reflects with the same sign.

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Option B: Infinity

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Option C: Equal to the incident voltage

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Option D: Twice the incident voltage

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