Electrical Engineering Conductors

Questions and Answers

What is the relationship between AC resistance and DC resistance for a conductor?

AC resistance is equal to DC resistance.

AC resistance is 1.1 times the DC resistance. (correct)

AC resistance is always lower than DC resistance.

AC resistance can never be accurately calculated.

In calculating the DC resistance for a copper conductor, which formula is used?

$R_{dc} = \rho \times A$

$R_{dc} = \frac{1}{\rho A}$

$R_{dc} = \frac{\rho}{A}$ (correct)

$R_{dc} = \frac{A}{\rho}$

What is primarily responsible for the difference in current density within a conductor's cross section?

Material differences

Temperature variation

Magnetic field

Skin effect (correct)

Which parameter is considered the most important for transmission lines?

Inductance Signup and view all the answers

How is the total AC resistance calculated for a length of conductor?

$R_{AC-total} = R_{DC} \times 1.1 \times L$ Signup and view all the answers

What is the effect of the inductive reactance on a transmission line?

It dominates the impedance element. Signup and view all the answers

Given a diameter of 3 cm for an aluminum conductor, what is the approximate cross-sectional area?

$7.069 \times 10^{-4} m^2$ Signup and view all the answers

If the resistivity of aluminum is given as $2.83 \times 10^{-8} \Omega m$, how do you calculate the DC resistance per meter?

$R_{DC} = \frac{2.83 \times 10^{-8}}{\pi \cdot (0.015)^2}$ Signup and view all the answers

What is the formula for calculating the dc resistance per phase of a transmission line?

$Rdc = \frac{ρ}{A}$ Signup and view all the answers

Why is aluminum preferred over copper for conductors in transmission lines?

Aluminum is lighter and more cost-effective Signup and view all the answers

What are the primary parameters studied to assess the performance of transmission lines?

Resistance, Inductance, Capacitance Signup and view all the answers

What is the main consequence of resistance in a transmission line?

Introduction of heat losses Signup and view all the answers

Which type of conductor is most commonly used in overhead transmission lines?

Aluminum conductor steel reinforced (ACSR) Signup and view all the answers

How does the skin effect influence conductors at high frequencies?

Current tends to flow more towards the surface of the conductor Signup and view all the answers

What role does inductance play in the performance of transmission lines?

It impacts the voltage regulation Signup and view all the answers

What is the typical insulation method used on conductors of overhead transmission lines?

No insulation is used Signup and view all the answers

What is the inductive reactance of a given transmission line operating at 50 Hz with an inductance of 6.25 mH?

1.96 ohm Signup and view all the answers

How does bundling conductors in extra high voltage (EHV) transmission lines primarily affect the performance?

Reduces electric field and corona losses Signup and view all the answers

In a transmission line with a conductor radius of 2.04 cm and spacing of 10 m, what is the approximate GMR?

0.0159 m Signup and view all the answers

Given the total inductance of 0.1875 H, what is the calculated length of a transmission line with equilateral triangle formation?

150 km Signup and view all the answers

What is the primary reason for using more than one conductor per phase in EHV transmission lines?

Reduce series impedance Signup and view all the answers

What is the formula used to calculate the line inductance for a transmission line given its characteristics?

$L = 2 \times 10^{-7} \ln \left(\frac{D_{eq}}{GMR} \right) \times length$ Signup and view all the answers

What contributes to increased losses in a conductor, which can be reduced by proper design in transmission lines?

Skin effect Signup and view all the answers

What is the inductance per unit length for the specified transmission line if the line inductance is given as 1.25 μH/m?

1.25 μH/m Signup and view all the answers

Study Notes

AC Resistance in Conductors

AC resistance differs from DC resistance due to varying current density in the conductor's cross-section.
AC resistance can be approximated as Rac ≈ 1.1Rdc, a relationship due to the skin effect.
Skin effect causes current to concentrate near the surface of the conductor, leading to higher AC resistance compared to DC.

Calculating AC Resistance for Copper Conductor

Resistivity of copper: 1.68 × 10⁻⁸ Ωm.
Cross-sectional area for calculation: 3 × 10⁻³ m².
DC resistance formula: Rdc = ρ / A, resulting in Rdc = 5.6 × 10⁻⁶ Ω/m.
Consequently, AC resistance calculated as Rac = Rdc × 1.1 = 6.16 × 10⁻⁶ Ω/m.
Converting per meter resistance to per kilometer results in Rac = 6.16 × 10⁻³ Ω/km.

Calculating AC Resistance for Aluminum Conductor

Resistivity of aluminum: 2.83 × 10⁻⁸ Ωm.
Diameter of conductor: 3 cm (0.03 m), converted to radius: 0.015 m.
Cross-sectional area calculated using A = πr² results in A ≈ 7.069 × 10⁻⁴ m².
DC resistance calculated as Rdc = ρ / A yielding Rdc = 4.003 × 10⁻⁵ Ω/m.
Resulting AC resistance is Rac = Rdc × 1.1 = 4.4033 × 10⁻⁵ Ω/m.
For a 10 km line, the total AC resistance is Rac-total = 0.44 Ω.

Inductance in Transmission Lines

Inductance (L) is a crucial parameter in transmission lines, influencing voltage drop and transmission capacity.
Inductive reactance (X) is calculated as X = ωL, with significant effects on line performance.
A current-carrying conductor generates a magnetic field that contributes to inductance.

Inductance Calculation Examples

Inductance per phase for a certain configuration found using Lph = 2 × 10⁻⁷ ln(Deq / GMR).
Example calculation gives Lph = 1.25 μH/m, total inductance for 5000 m = 6.25 mH.
The corresponding inductive reactance X = 1.96 ohm at 50 Hz.

Calculating Line Inductance and Reactance

Inductance for a completely transposed line with specified parameters leads to a calculated GMR.
For a transmission line with total inductance of 0.1875 H, the line length is determined to be 150 km using the formulation.

Bundling Conductors

Bundling involves using multiple conductors per phase to lower series impedance and enhance power transmission.
Benefits of bundling include increased transmitted power and reduced electric fields, minimizing corona losses and noise.

Common Transmission Line Voltages

Voltage levels for transmission lines typically include 66 kV, 132 kV, 220 kV, 400 kV, and 765 kV among others.

Insulators and Material Use

Cap and pin insulators are primarily made from porcelain or glass; strings of such insulators isolate high voltages.
Aluminum conductors are favored over copper for their lighter weight and cost-effectiveness.
Stranded conductors are more flexible and efficient for larger sizes compared to solid conductors.

Overhead Transmission Line Conductors

Conductors used in overhead lines are typically bare, relying on air as insulation.
Understanding transmission line parameters such as resistance, inductance, and capacitance is essential for evaluating performance and efficiency in electrical systems.

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Description

Explore the concepts of ac and dc resistance in electrical conductors through this quiz. You'll learn about the skin effect and how the current density varies within the conductor's cross-section. Test your understanding of resistance calculations and manufacturer tables.