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The coefficient of reflection for current for an open ended line is

0.5

– 1.0

Zero

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option C

– 1.0

Quick Summary:

In an open-ended transmission line, the termination is an infinite impedance ( $Z_L = \infty$ ). Consequently, when a current wave reaches the end, it must be fully reflected in the opposite direction to maintain the boundary condition of zero net current, resulting in a reflection coefficient of $-1.0$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\\rho_i = \frac{Z_0 - Z_L}{Z_0 + Z_L}$ — General formula for current reflection coefficient

$\\rho_v = \frac{Z_L - Z_0}{Z_L + Z_0}$ — General formula for voltage reflection coefficient

⚙️ Working Principle

The reflection coefficient for current ( $\\rho_i$ ) is defined by the formula $\\rho_i = \frac{Z_0 - Z_L}{Z_0 + Z_L}$ , where $Z_0$ is the characteristic impedance and $Z_L$ is the load impedance. As $Z_L \to \infty$ , the expression simplifies: $\\lim_{Z_L \to \infty} \frac{Z_0/Z_L - 1}{Z_0/Z_L + 1} = \frac{0 - 1}{0 + 1} = -1$ . This reversal ensures the current at the open circuit remains zero, obeying Kirchhoff's current law.

📌 Key Points

▸
At an open-circuit termination, voltage reflection coefficient is $+1.0$ (doubling voltage).
▸
At an open-circuit termination, current reflection coefficient is $-1.0$ (canceling current).
▸
Reflection occurs due to the mismatch between line impedance $Z_0$ and termination impedance $Z_L$ .

✅ Advantages

▸
Prevents current flow into an open branch
▸
Essential for analyzing transient overvoltages

❌ Disadvantages / Limitations

▸
Causes standing waves on the transmission line
▸
Can lead to high voltage stress at the open end

🛠️ Applications / Uses

▸
Fault analysis in power systems
▸
Communication line impedance matching
▸
Time Domain Reflectometry (TDR)

🔄 Comparison Table

Feature	Open Circuit ($Z_L = \infty$)	+1.0
Termination Type	Voltage Reflection ( $\rho_v$ )	Current Reflection ( $\rho_i$ )
Termination Type	Voltage Reflection ( $\rho_v$ )	Current Reflection ( $\rho_i$ )

📄 Additional Information

▸
In power systems, the open-ended line condition occurs during switching operations or at the end of a radial feeder without a connected load.
▸
Option D (Zero) is the coefficient for a matched load where $Z_L = Z_0$ .

📊 Diagram / Illustration

✅

C is correct — The reflection coefficient for current at an open-ended line is $-1.0$ because the current must sum to zero at the open boundary.

Core Concepts Used

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Traveling wave theory Impedance mismatch Boundary conditions in power systems

💡 EXAM TIP

Always remember that for open circuits, voltage reflects in phase ( $\rho=1$ ) while current reflects out of phase ( $\rho=-1$ ); for short circuits, it is the exact opposite.

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