Resistance Calculations in Electrical Conductors Quiz
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Questions and Answers

What is the equation for the DC resistance of a conductor at temperature T?

  • $R_{dc,T} = \frac{A}{\rho_T l}$
  • $R_{dc,T} = \frac{\rho_T l}{A}$ (correct)
  • $R_{dc,T} = \frac{\rho_T A}{l}$
  • $R_{dc,T} = \frac{l}{A\rho_T}$

What are the SI units for resistivity?

  • Wm (correct)
  • W-cmil/ft x 10^-8
  • Wm x 10^-8
  • W-cmil/ft

What is the temperature constant for copper?

  • 61%
  • 234.5
  • 17.2%
  • 100% (correct)

What factor makes the dc resistance of a stranded conductor 1 or 2% larger than the calculated resistance?

<p>Spiraling (B)</p> Signup and view all the answers

What is the equation for DC resistance (Rdc) of a conductor?

<p>$R_{dc} = \frac{\rho_T l}{A}$ (D)</p> Signup and view all the answers

What is the effect of frequency on current distribution in a solid cylindrical conductor for AC?

<p>Current tends to crowd toward the conductor surface (A)</p> Signup and view all the answers

In the equation for DC resistance (Rdc), what does A represent?

<p>Cross-sectional area (D)</p> Signup and view all the answers

How does the resistivity of a conductor change with temperature according to the given information?

<p>Resistivity increases with increasing temperature (B)</p> Signup and view all the answers

What is the effect of current magnitude on resistance for magnetic conductors?

<p>Resistance increases with increasing current magnitude (C)</p> Signup and view all the answers

What is the equation for the skin effect phenomenon?

<p>$I = \frac{1}{r}$ (A)</p> Signup and view all the answers

What is the formula to calculate the total copper cross-sectional area (A) for 12 strands of a given diameter?

<p>$A = 12 \pi (\frac{d}{2})^2$ (B)</p> Signup and view all the answers

How does the resistance of ACSR conductors change with current magnitude compared to steel conductors?

<p>Resistance of ACSR conductors increases less than steel conductors with increasing current magnitude (A)</p> Signup and view all the answers

According to the given information, the resistance of a stranded conductor is 1 or 2% larger than that calculated from the equation $R_{dc,T} = rac{ρ_T l}{A}$ due to _______.

<p>spiraling</p> Signup and view all the answers

The equation for the DC resistance of a conductor at temperature T is _______.

<p>$R_{dc,T} = rac{ρ_T l}{A}$</p> Signup and view all the answers

The temperature constant for copper is _______.

<p>3.93 x 10^{-3} Ω·cm/°C</p> Signup and view all the answers

AC resistance or effective resistance of a conductor is given by the equation:

<p>R_{\text{dc},T} = \dfrac{\rho_T l}{A} \Omega</p> Signup and view all the answers

The resistivity of iron at 20°C is _______.

<p>10.37 Wm x 10^{-8} or 1.59 Ω·cm</p> Signup and view all the answers

Total copper cross-sectional area (A) in mm2 is given by the equation:

<p>A = 12 \pi r^2 = 12 \pi \left(\dfrac{d}{2}\right)^2 = 12 \pi \left(\dfrac{3.373 \text{ mm}}{2}\right)^2 = 107.23 \text{ mm}^2</p> Signup and view all the answers

The resistivity at 20°C for hard-drawn copper is

<p>1.77$ W-cmil/ft</p> Signup and view all the answers

The equation to calculate the DC resistance of a conductor at temperature T is

<p>R_{\text{dc},T} = \dfrac{\rho_T l}{A} \Omega</p> Signup and view all the answers

The equation for the DC resistance of a conductor at 50°C with a length of 1 km is given by:

<p>R_{\text{dc},50°C} = \left[\left(1.973 \times 10^{-8} \Omega\text{m}\right) \times \left(\dfrac{103 \times 1.02 \text{ m}}{107.23 \text{ mm}^2}\right)\right] = 0.1877 \Omega/\text{km}</p> Signup and view all the answers

The temperature constant for copper is listed in

<p>Table 4.3</p> Signup and view all the answers

The resistivity at 20°C for aluminum is

<p>2.83$ W-cmil/ft</p> Signup and view all the answers

The resistivity at 20°C for steel is

<p>61$ W-cmil/ft</p> Signup and view all the answers

According to the given information, the resistance of a stranded conductor is 1 or 2% larger than that calculated from the equation $R_{dc,T} = \frac{\rho_T l},{A}$ due to

<p>spiraling</p> Signup and view all the answers

The equation for the DC resistance of a conductor at temperature T is

<p>$R_{dc,T} = \frac{\rho_T l},{A}$</p> Signup and view all the answers

The resistivity of iron at 20°C is

<p>9.6</p> Signup and view all the answers

The equation for the skin effect phenomenon is

<p>$\text{ac resistance or effective resistance} = R_{dc} \sqrt{1 + (2 \pi f \rho)/\mu}$</p> Signup and view all the answers

Total copper cross-sectional area (A) in mm2 is given by the equation

<p>$A = 12 \pi r^2$</p> Signup and view all the answers

Rdc at 50o C with length of 1 km. Use hard-drawn copper, assume a 2% increase in resistance due to Spiraling

<p>0.1877 Ω / km</p> Signup and view all the answers

The equation for the DC resistance of a conductor at 50°C with a length of 1 km is given by

<p>$R_{dc,50°C} = \rac{ρ_{T} l},{A}$</p> Signup and view all the answers

The equation for the skin effect phenomenon is

<p>For AC, the current distribution is non-uniform.</p> Signup and view all the answers

The equation for DC resistance (Rdc) of a conductor is

<p>$R_{dc,T} = \rac{ρ_{T} l},{A}$</p> Signup and view all the answers

The resistivity at 20°C for hard-drawn copper is

<p>1.77 x 10^{-8} Ωm</p> Signup and view all the answers

The resistivity at 20°C for steel is

<p>10.37 x 10^{-8} Ωm</p> Signup and view all the answers

What are the main factors affecting insulator leakage current?

<p>Amount of dirt, salt, and other contaminants, and meteorological factors (A)</p> Signup and view all the answers

The temperature constant for copper is listed in

<p>Table 4.3</p> Signup and view all the answers

What causes corona loss in overhead lines?

<p>Electrically ionized air due to high electric field strength at conductor surface (C)</p> Signup and view all the answers

Why is conductance usually neglected in power system studies?

<p>It is a very small component of the shunt admittance (D)</p> Signup and view all the answers

What is the main cause of power loss due to corona?

<p>High electric field strength at conductor surface causing air ionization (C)</p> Signup and view all the answers

Why is conductance usually neglected in power system studies?

<p>It is a very small component of the shunt admittance (C)</p> Signup and view all the answers

What factor primarily determines the insulator leakage current?

<p>Accumulation of dirt, salt, and contaminants on insulators (A)</p> Signup and view all the answers

Flux linkage inside the conductor is denoted by the symbol λ

<p>True (A)</p> Signup and view all the answers

The equation to calculate inductance from flux linkages per ampere is $L = \frac{\lambda}{I}$

<p>True (A)</p> Signup and view all the answers

The permeability of free space, $\mu_0$, is equal to $4\pi \times 10^{-7} H/m$

<p>True (A)</p> Signup and view all the answers

The magnetic flux density B can be calculated using the equation $B = \mu H$

<p>True (A)</p> Signup and view all the answers

What is the equation to calculate the magnetic flux density B?

<p>$B = \mu H$ (C)</p> Signup and view all the answers

What is the equation to calculate inductance from flux linkages per ampere?

<p>$L = \frac{\lambda}{I}$ (C)</p> Signup and view all the answers

What is the unit of magnetic flux density B?

<p>All of the above (D)</p> Signup and view all the answers

What is the permeability of free space, $\mu_0$, equal to?

<p>$4\pi \times 10^{-7} H/m$ (A)</p> Signup and view all the answers

Calculate the inductance of each conductor due to both internal and external flux linkages.

<p>The inductance of each conductor due to both internal and external flux linkages is given by $Lx = Ly = 2 \times 10^{-7} \ln \left( \frac{D},{r'} \right) , \text{H/m}$, which can be converted to mH/km by multiplying by 1000.</p> Signup and view all the answers

What is the total inductance of the line with a 60-Hz single-phase, two-wire overhead line?

<p>The total inductance of the line, denoted as $L$, is the sum of inductance of each conductor: $L = Lx + Ly = 0.8899 + 0.8899 = 1.780 , \text{mH/km}$ per circuit.</p> Signup and view all the answers

What is the formula to calculate the inductance of each conductor due to both internal and external flux linkages?

<p>The inductance of each conductor due to both internal and external flux linkages is given by $Lx = Ly = 2 \times 10^{-7} \ln \left( \frac{D},{r'} \right) , \text{H/m}$, where $D$ is the spacing between conductors and $r'$ is the effective radius of the conductor.</p> Signup and view all the answers

What is the equation for the total inductance of a single-phase circuit?

<p>The total inductance of the single-phase circuit, called loop inductance, is not provided in the given text.</p> Signup and view all the answers

What is the equation to calculate the inductance of each conductor due to internal flux linkages only?

<p>The equation to calculate the inductance of each conductor due to internal flux linkages only is $Lint = \frac{1}{2} \times 10^{-7} H/m = 0.05 mH/Km$ per conductor.</p> Signup and view all the answers

In Example 1, what is the inductance of each conductor due to internal flux linkages only?

<p>In Example 1, the inductance of each conductor due to internal flux linkages only is 0.05 mH/Km per conductor.</p> Signup and view all the answers

What is the flux linkage in phase a conductor for a three-phase three-wire line?

<p>The flux linkage in phase a conductor for a three-phase three-wire line is not provided in the given text.</p> Signup and view all the answers

Calculate in mH/km b) the inductance of each conductor due to both internal and external flux linkages

<p>0.8899 mH/Km per conductor</p> Signup and view all the answers

Calculate in mH/km c) the total inductance of the line

<p>1.780 mH/Km per circuit</p> Signup and view all the answers

The conductors are arranged in a horizontal configuration with 0.5 m spacing between conductors. Calculate in mH/km b) the inductance of each conductor due to both internal and external flux linkages

<p>0.8899 mH/Km per conductor</p> Signup and view all the answers

Flux linkage in phase a conductor for a three-phase three-wire line is denoted by the symbol

<p>\lambda_{a}$</p> Signup and view all the answers

Total inductance of the line with a 60-Hz single-phase, two-wire overhead line is denoted by the symbol

<p>L_{total}</p> Signup and view all the answers

Calculate in mH/km c) the total inductance of the line

<p>$L_{total} = 2 \times L_{int}$</p> Signup and view all the answers

In Example 1, the inductance of each conductor due to internal flux linkages only is denoted by the symbol

<p>L_{int}</p> Signup and view all the answers

Inductance is the property of a circuit that opposes any change in ______

<p>current</p> Signup and view all the answers

The total inductance of the single-phase circuit, called loop inductance, is represented by the symbol ______

<p>L</p> Signup and view all the answers

The inductance of phase a is represented by the symbol ______

<p>La</p> Signup and view all the answers

The inductance of each conductor due to internal flux linkages only is calculated using the formula ______

<p>Lint = \frac{1}{2} \times 10^{-7} \frac{H}{m} = 0.05 \frac{mH}{Km} per conductor</p> Signup and view all the answers

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