Physics Chapter on Current and Ohm's Law

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Questions and Answers

What does Ohm's Law describe?

The direct proportionality of current density to electric field for certain materials. (correct)

The behavior of all materials under electrical conditions.

The relationship between voltage and resistance only.

The inverse relationship between current density and electric field.

Which factor primarily affects the resistivity of a conductor?

The material of the conductor. (correct)

The length of the conductor.

The voltage applied across the conductor.

The cross-sectional area of the conductor.

If the temperature of a conductor increases, what happens to its resistivity?

It increases. (correct)

It becomes zero.

It decreases.

It remains constant.

What is the relationship between resistance and resistivity if resistivity is constant?

Resistance also remains constant. Signup and view all the answers

What happens to current density in a semiconductor if the electric field is maintained while lowering its temperature?

It decreases. Signup and view all the answers

What is the SI unit for resistivity?

Ohm meter Signup and view all the answers

When is a material considered ohmic?

When it follows Ohm's Law. Signup and view all the answers

What is the effect of a material's temperature coefficient of resistivity on its resistivity?

It modifies the resistivity according to temperature changes. Signup and view all the answers

What is the relationship between resistance and temperature described in the equation 𝑅(𝑇) = 𝑅0[1 + 𝛼(𝑇 − 𝑇0)]?

Resistance increases linearly with temperature. Signup and view all the answers

How is the resistivity of a wire calculated from its resistance?

𝜌 = 𝑅 × 𝐴 / 𝐿 Signup and view all the answers

If the voltage across a copper wire is doubled, how is the current affected?

Current doubles. Signup and view all the answers

What is the primary factor that prevents the escape of electrons from a conductor without an internal electric field?

The random motion of electrons Signup and view all the answers

What does electromotive force (EMF) represent in a circuit?

The energy per unit charge. Signup and view all the answers

Which statement correctly describes the purpose of a resistor in a circuit?

To create a specific resistance value. Signup and view all the answers

What is the drift velocity of electrons in copper as stated?

$1.079 \times 10^{-4} \ m/s$ Signup and view all the answers

How does current density (J) relate to the drift velocity (vd)?

$J = n \times q \times v_{d}$ Signup and view all the answers

Which factor affects the resistance of a wire?

The material and cross-sectional area of the wire. Signup and view all the answers

Why is it important to distinguish that electromotive force is not a force?

It clarifies that units of EMF and potential difference are the same. Signup and view all the answers

What unit is equivalent to 1 C/s?

Ampere Signup and view all the answers

What happens to the potential energy in a conductor during a complete circuit?

It increases at certain points due to the EMF source. Signup and view all the answers

In a current-carrying wire, how is current defined?

As the total charge flowing per unit time Signup and view all the answers

What is the expression for calculating the current (I) in a conductor?

$I = \frac{dQ}{dt}$ Signup and view all the answers

What does a positive internal electric field in a conductor do to free electrons?

Accelerates them in one direction Signup and view all the answers

If a copper wire has a cross-sectional area of $2.05 \times 10^{-3} m^2$ and carries a current of 4.85 A, what is the current density?

$1.469 \times 10^{6} A/m^2$ Signup and view all the answers

What is the formula used to calculate electric power in relation to resistance?

$P = \frac{V^2}{R}$ Signup and view all the answers

In calculating the electric field across a cylindrical cable, what is the derived value when using a 220-V potential difference?

0.147 V/m Signup and view all the answers

What is the required diameter of a cylindrical copper cable to produce heat at 75.0 W?

0.184 mm Signup and view all the answers

What is the relationship between the resistivity, length, and diameter of a cylindrical conductor when determining its resistance?

$R = \frac{\rho L}{A}$ where $A = \pi r^2$ Signup and view all the answers

If a cylindrical cable has a length of 1500 m and is defined by a specific resistivity, what variable does not affect the production of heat in this context?

Conductive material type Signup and view all the answers

What is the relationship between terminal voltage and electromotive force for a real EMF source?

Terminal voltage is less than the electromotive force due to internal resistance. Signup and view all the answers

If a 5.0 V battery with an internal resistance of 0.5 Ω is connected to a 2.0-Ω resistor, what current flows through the resistor?

1.5 A Signup and view all the answers

What happens to the reading on an ideal voltmeter connected in a circuit with an open circuit condition?

The reading on the voltmeter will show the electromotive force. Signup and view all the answers

For a battery with an emf of 12.0 V and an internal resistance of 0.40 Ω, what resistance will yield a power dissipation of 80.0 W?

6.0 Ω Signup and view all the answers

How is power dissipated in a resistor expressed in terms of voltage and current?

P = V^2/R Signup and view all the answers

In a closed circuit with both EMF and internal resistance, what is the expected voltage drop across the internal resistance?

It equals the product of current and internal resistance (Ir). Signup and view all the answers

If the internal resistance is increased in a circuit with constant EMF, what happens to the terminal voltage?

The terminal voltage decreases. Signup and view all the answers

What is a characteristic of an ideal voltmeter in a circuit?

It has no effect on the circuit it is connected to. Signup and view all the answers

Study Notes

Current

Current is the motion of charge from one region to another.
For a conductor with no internal electric field, there is no net flow of charge, resulting in no current.
For a conductor with an internal electric field, free electrons accelerate in the direction of the force, but collisions with ions cause them to change direction. This slow, net motion is called drift motion.
Current is not a vector quantity. It is always along the length of the wire, even when curved.

Current Density

Current density (J) is the current per unit cross-sectional area.
It is calculated as: J = I/A = nqv_d, where v_d is the drift velocity, q is the magnitude of the charge, and n is the concentration of particles.
The SI unit of current density is 1 C/s∙m² or 1 A/m².

Ohm's Law

Ohm's Law states that current density is directly proportional to the electric field.
The ratio of electric field to current density is constant and is called resistivity (ρ).
Ohm's Law is an idealized model that describes the behavior of some materials well but is not universally applicable.
Materials that obey Ohm's Law are called ohmic or linear conductors.

Resistivity

Resistivity is the ratio of the magnitudes of electric field and current density: ρ = E/J.
It is a measure of a material's resistance to the flow of current. Good conductors have low resistivity, while good insulators have high resistivity.
Resistivity depends on the type of material and temperature.
The SI unit of resistivity is 1 Ω∙m.

Conductivity

Conductivity is the reciprocal of resistivity.
It is a measure of a material's ability to conduct electricity.
The SI unit of conductivity is 1/ Ω∙m.

Resistance

Resistance (R) is the relationship between resistivity, length, and cross-sectional area of a conductor: R = ρL/A.
Resistance is also related to voltage (V) and current (I): R = V/I.
This relationship is another way to express Ohm's Law.
The SI unit of resistance is 1 Ohm (Ω).

Electromotive Force (EMF)

EMF is the energy per unit charge that a device provides to a circuit.
Examples of EMF sources include batteries, generators, solar cells, thermocouples, and fuel cells.
EMF is not a force but a potential difference.
The terminal voltage (V_ab) of a real EMF source is less than its EMF due to internal resistance (r): V_ab = ξ - Ir.

Energy and Power in Circuits

Power (P) is the rate at which energy is delivered to or extracted from a circuit element: P = V_abI.
The SI unit of power is 1 Watt (W).
Power dissipated in a resistor: P = V_abI = I²R = V_ab²/R.

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Description

Explore the concepts of electric current, current density, and Ohm's Law in this quiz. Understand how charge flows in conductors, the relationship between current density and electric field, and the underlying principles governing these phenomena. Test your knowledge with practical examples and calculations.