Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

Quick Summary:

The current reflection coefficient ( $\rho_i$ ) for an open-ended transmission line is 1. This implies that when a current wave hits an open circuit, it reflects with the same polarity and magnitude, resulting in a net current of zero at the termination point.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

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

$\rho_i = 1$ — Specifically for an open-ended line ( $Z_L = \infty$ )

⚙️ Working Principle

When a traveling wave reaches an impedance discontinuity, it must satisfy boundary conditions. For an open circuit, the load impedance $Z_L \to \infty$ . The current reflection coefficient is defined as $\rho_i = \frac{Z_0 - Z_L}{Z_0 + Z_L}$ . As $Z_L \to \infty$ , the limit yields $\rho_i = -1$ for voltage reflection, but for current, the boundary condition requires the total current to be zero, leading to a reflection coefficient of 1 to cancel the incident wave.

📌 Key Points

▸
For an open-ended line, current reflection is total and in-phase ( $\rho_i = 1$ ).
▸
Voltage reflection coefficient for an open-ended line is 1, causing the voltage to double at the termination.
▸
Current reflection coefficient for a short-circuited line is -1, causing current to double.
▸
The reflection coefficient depends solely on the ratio of line impedance to load impedance.

✅ Advantages

▸
Predictable behavior of transients at line terminals.
▸
Facilitates calculation of standing wave patterns in power systems.

❌ Disadvantages / Limitations

▸
High voltage reflections at open ends can lead to insulation breakdown.
▸
Current doubling at short-circuit ends can cause mechanical stress on conductors.

🛠️ Applications / Uses

▸
Fault analysis in high-voltage transmission lines.
▸
Design of protective relaying schemes.
▸
Surge arrester placement strategies.

🔄 Comparison Table

Feature	Open Circuit	Short Circuit
Termination Type	Current Reflection ( $\rho_i$ )	Voltage Reflection ( $\rho_v$ )

📄 Additional Information

▸
When $Z_L = Z_0$ , the reflection coefficient is 0, implying a perfectly matched line with no reflections.
▸
Option B (1) is identical to A; Option D (Zero) is the coefficient for a matched line.

📊 Diagram / Illustration

✅

A is correct — The current reflection coefficient for an open-ended transmission line is 1.

Core Concepts Used

Click any tag to open in AI Tutor

Traveling Wave Theory Reflection Coefficient Transmission Line Impedance

💡 EXAM TIP

Remember: Voltage reflection coefficient is $\frac{Z_L - Z_0}{Z_L + Z_0}$ , while current reflection is $\frac{Z_0 - Z_L}{Z_0 + Z_L}$ . They are negatives of each other.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)