Physics Chapter 27: Current and Resistance
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Questions and Answers

What is the drift speed of electrons in copper as calculated in the document?

  • $5.57 \times 10^{-5}$ m/s (correct)
  • $3.45 \times 10^{-5}$ m/s
  • $4.75 \times 10^{-5}$ m/s
  • $6.29 \times 10^{-5}$ m/s

    • What is the expression for current density in terms of current and cross-sectional area?

  • $J = \frac{I}{A}$ (correct)
  • $J = I + A$
  • $J = \frac{I}{2A}$
  • $J = I \times A$

    • At time $t = 1$ s, what is the instantaneous current as given in the document?

  • 5 A
  • 12 A
  • 10 A
  • 17 A (correct)

    • What is the calculated current density for a current of 17 A and cross-sectional area of $2 \times 10^{-4}$ m²?

    <p>85 kA/m² (A)</p> Signup and view all the answers

    From Ohm's law, the expression for current can be defined as which of the following?

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

    Given the resistivity of tungsten, what is the resistance calculated for a specific configuration?

    <p>1.4 Ω (B)</p> Signup and view all the answers

    What is the role of drift speed in the conduction of electricity?

    <p>It decreases with an increase in electron density. (B)</p> Signup and view all the answers

    What physical quantity does the symbol 𝜌 represent in the resistance calculations?

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

    What happens to the resistivity of a conductor as temperature increases?

    <p>Resistivity increases due to more collisions. (D)</p> Signup and view all the answers

    What does the temperature coefficient of resistivity (α) indicate?

    <p>The resistivity changes at a linear rate with temperature. (C)</p> Signup and view all the answers

    Which equation represents the relationship of resistance and temperature?

    <p>$R = ho l / A$ (A)</p> Signup and view all the answers

    In the equation $I = \frac{\Delta V}{R}$, what does I represent?

    <p>Current flowing through the circuit. (A)</p> Signup and view all the answers

    What occurs to the resistivity of semiconductors with temperature according to the discussion?

    <p>Decreases with increased temperature. (D)</p> Signup and view all the answers

    What characterizes the nonlinear region of resistivity in metals at low temperatures?

    <p>Effects of impurities and imperfections. (B)</p> Signup and view all the answers

    What does the equation $\rho = \rho_0 (1 + \alpha (T - T_0))$ describe?

    <p>The relationship between resistivity, temperature, and temperature coefficient. (B)</p> Signup and view all the answers

    What process does electrical power describe in a circuit?

    <p>The rate of energy transfer from one component to another. (C)</p> Signup and view all the answers

    What is the formula used to calculate the resistance of a material based on resistivity?

    <p>R = ρl / A (B)</p> Signup and view all the answers

    Given the resistivity of aluminum (𝜌𝐴𝑙) is $2.82 × 10^{-8} Ω m$, what is its unit in the International System of Units?

    <p>Ohm-meter (B)</p> Signup and view all the answers

    What is the value of the fractional change in resistance (f) when α = $5 × 10^{-3} ℃^{-1}$, T = 50, and T0 = 25?

    <p>0.12 (C)</p> Signup and view all the answers

    If the resistance of a silver wire is calculated using the given α for silver as $3.8 × 10^{-3} ℃^{-1}$, what is the resistance when R0 is 6 Ω and the temperature changes from 20°C to 34°C?

    <p>6.32 Ω (B)</p> Signup and view all the answers

    What does the variable α represent in the resistance equation?

    <p>Temperature Coefficient of Resistance (D)</p> Signup and view all the answers

    How is current (I) found using power (P) and voltage (∆V) in a resistor?

    <p>I = P / ∆V (B)</p> Signup and view all the answers

    What is the equivalent resistance (R) if the power (P) is 120 Watts and the voltage (∆V) is 1000 Volts?

    <p>14.4 Ω (D)</p> Signup and view all the answers

    What relationship does decreasing the area (A) of a material have on its resistance (R) when the resistivity and length remain constant?

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

    What is the effect of temperature on the resistance of a conductor if the temperature coefficient (α) is positive?

    <p>Resistance increases with temperature (D)</p> Signup and view all the answers

    Which equation accurately defines the change in resistance (R) considering initial resistance (R0), temperature change (T - T0), and temperature coefficient (α)?

    <p>R = R0 + αR0(T - T0) (A)</p> Signup and view all the answers

    Flashcards

    Resistance of aluminum

    The resistance of aluminum is 2.82 x 10^-8 Ω.m

    Resistance of copper

    The resistance of copper is 1.7 x 10^-8 Ω.m

    Resistance formula

    Resistance (R) = (resistivity (ρ) * length (l)) / area (A)

    Relationship between aluminum and copper radius

    The ratio of radii of aluminum and copper is equal to the square root of the ratio of their resistivities. (r_Al/r_Cu)² = (ρ_Al/ρ_Cu)

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    Thermal resistance coefficient of iron

    The thermal expansion coefficient of iron (α) is 5 x 10^-3 °C^-1.

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    Resistance change with temperature formula

    R = R₀ * [1 + α * (T - T₀)]

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    Fractional resistance change

    f = (R - R₀) / R₀

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    Resistance of silver coefficient

    The thermal coefficient of silver is 3.8 x 10^-3 °C^-1

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    Power in Resistor Equation

    Power (P) = Current (I) * Voltage (ΔV)

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    Resistance from Power Equation

    Resistance (R) = (Voltage (ΔV)² ) / Power (P)

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    Drift speed (vd)

    The average velocity of electrons in a conductor due to an electric field.

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    Current in a conductor (I)

    The rate of flow of electric charge through a cross-section of a conductor.

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    Current density (J)

    The current flowing per unit area of a conductor.

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    Resistivity (ρ)

    A material's resistance to the flow of electric current.

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    Resistance (R)

    Opposition to the flow of electric current in a conductor.

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    Ohm's Law

    The mathematical relationship between voltage, current, and resistance; V = IR.

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    Instantaneous current

    The current at a specific point in time.

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    Cross-sectional area (A)

    The area of a two-dimensional cross-section of an object.

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    Resistivity and Temperature

    The resistivity of a conductor changes with temperature. As temperature increases, collisions between electrons and atoms increase, causing resistivity to rise.

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    Resistivity Equation

    The resistivity of a conductor at a given temperature can be calculated with the formula: 𝜌 = 𝜌0 (1 + 𝛼(𝑇 − 𝑇0)) where 𝜌0 is the resistivity at reference temperature 𝑇0, 𝛼 is the temperature coefficient of resistivity, and 𝑇 is the current temperature.

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    Temperature Coefficient of Resistivity

    A material's temperature coefficient of resistivity (𝛼) describes how much its resistivity changes for each degree Celsius change in temperature.

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    Semiconductors and Resistivity

    Semiconductors have a unique behavior: their resistivity decreases with increasing temperature. This is unlike metals, where resistivity increases.

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    Resistance and Temperature Relationship

    Since resistance is directly proportional to resistivity, changing temperature also changes resistance. The formula 𝑅 = 𝑅0 (1 + 𝛼(𝑇 − 𝑇0)) shows this relationship.

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    Power in a Circuit

    Power is the rate at which energy is transferred in a circuit. For a simple circuit with a battery and a resistor, energy is transferred from the battery to the resistor.

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    Electrical Power Equation

    In a circuit, the power dissipated by a resistor is given by: P = I * ΔV where P is power, I is current, and ΔV is voltage across the resistor.

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    Study Notes

    Chapter 27: Current and Resistance

    • This chapter covers electric current, resistance, resistance and temperature, and electrical power.

    27.1 Electric Current

    • Charges moving perpendicular to a surface of area A create an average current.
    • Average current (Iavg) = ΔQ/Δt, where ΔQ is the charge passing through A in time Δt.
    • Instantaneous current (I) = dQ/dt, the rate of change of charge flow.
    • SI unit of current is the ampere (A), 1 A = 1 C/s.
    • Conventional current direction is the direction positive charges would flow.
    • In conductors, current is due to electron motion, opposite to electron flow.
    • In gases and electrolytes, both positive and negative ions carry charge.

    27.2 Resistance

    • Current density (J) = I/A, the current per unit area, a uniform current.
    • Electric field (E) exists in a conductor whenever there's a potential difference across it.
    • Ohm's Law: For many materials (especially metals), the ratio of current density to electric field (σ) is constant. J = σE.
    • Conductivity (σ) is a material property of Ohmic materials.
    • Non-ohmic materials do not obey Ohm's Law.
    • Resistance (R) = pl/A, where p is resistivity, l is the length, and A is the cross-sectional area.
    • SI unit for R is Ohm (Ω)

    27.4 Resistance and Temperature

    • Resistivity (p) varies with temperature in most materials.
    • ρ = ρ0[1 + α(T - T0)], where ρ0 is resistivity at reference temperature T0 (often 20°C) and α is the temperature coefficient of resistivity.
    • Ideal conductors have zero resistivity.
    • Ideal insulators have infinite resistivity.

    27.6 Electrical Power

    • Power is the rate of energy transfer.
    • P = IΔV = I2R = ΔV2/R, where P is power, I is current, ΔV is potential difference, and R is resistance.
    • SI unit for power is Watt (W), 1 W = 1 J/s.

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    Chapter 27: Current and Resistance Physics PDF

    Description

    This quiz covers key concepts in Chapter 27, focusing on electric current and resistance. It includes understanding average and instantaneous current, resistance and temperature, and the principles of electric power. Test your knowledge of these fundamental topics in electricity.

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