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?

85 kA/m² Signup and view all the answers

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

$I = \frac{\Delta V}{R}$ Signup and view all the answers

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

1.4 Ω Signup and view all the answers

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

It decreases with an increase in electron density. Signup and view all the answers

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

Resistivity Signup and view all the answers

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

Resistivity increases due to more collisions. Signup and view all the answers

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

The resistivity changes at a linear rate with temperature. Signup and view all the answers

Which equation represents the relationship of resistance and temperature?

$R = ho l / A$ Signup and view all the answers

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

Current flowing through the circuit. Signup and view all the answers

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

Decreases with increased temperature. Signup and view all the answers

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

Effects of impurities and imperfections. Signup and view all the answers

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

The relationship between resistivity, temperature, and temperature coefficient. Signup and view all the answers

What process does electrical power describe in a circuit?

The rate of energy transfer from one component to another. Signup and view all the answers

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

R = ρl / A 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?

Ohm-meter 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?

0.12 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?

6.32 Ω Signup and view all the answers

What does the variable α represent in the resistance equation?

Temperature Coefficient of Resistance Signup and view all the answers

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

I = P / ∆V 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?

14.4 Ω 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?

Increases Resistance 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?

Resistance increases with temperature 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)?

R = R0 + αR0(T - T0) Signup and view all the answers

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 (I_avg) = 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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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.