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</p> Signup and view all the answers

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

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

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

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

    What is the equation for the skin effect phenomenon?

    <p>$I = \frac{1}{r}$</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>$A = 12 \pi (\frac{d}{2})^2$</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</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</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</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</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</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</p> Signup and view all the answers

    What factor primarily determines the insulator leakage current?

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

    Flux linkage inside the conductor is denoted by the symbol λ

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

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

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

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

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

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

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

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

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

    What is the unit of magnetic flux density B?

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

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

    <p>$4\pi \times 10^{-7} H/m$</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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