Electric Current and Conductors

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Questions and Answers

What is the drift velocity (vd) in a copper wire, given a current of 0.2 A, a cross-sectional area of 0.5 mm², and a free electron density of 8.4 x 10²⁸ m⁻³?

0.03 x 10⁻³ m/s

How many electrons flow per second through a conductor when a current of 32 A flows through it?

2 x 10²⁰ electrons

Derive the expression for resistivity (ρ) in terms of electron density (n), electronic charge (e), and mean free time (τ).

$ρ = \frac{1}{σ} = \frac{1}{neτ}$

Why is current density a vector while current is a scalar?

Current density is a vector defined as $J = \sigma E$ and depends on the direction of $\bar{E}$, while current is a scalar and is not direction-dependent. Signup and view all the answers

What is the mathematical relationship between current (I), charge (q), and time (t)?

$I = \frac{q}{t}$ Signup and view all the answers

Explain Ohm's law in terms of current density (J) and electric field (E).

$J = \sigma E$ Signup and view all the answers

What are free electrons and why are they significant in metals?

Free electrons are electrons loosely bound to the nucleus of atoms in metals, allowing them to move easily. They are significant because they enable the metal to conduct electric current. Signup and view all the answers

What happens to the motion of free electrons in a conductor when there is no potential difference applied?

The free electrons move randomly and there is no net transfer of charges, hence no current. Signup and view all the answers

Describe how a battery creates a potential difference across a conductor.

A battery creates a potential difference by having a positive terminal and a negative terminal, causing free electrons to drift towards the positive terminal. Signup and view all the answers

Why does water flow from higher gravitational potential to lower gravitational potential in the analogy given?

Water flows from higher to lower gravitational potential due to gravity acting on it. Signup and view all the answers

In the context of electric current, what does it mean for a region to have higher electric potential?

A region with higher electric potential has more positive charge or fewer electrons compared to a region with lower electric potential. Signup and view all the answers

What is the role of free electrons in producing electric current when potential difference is applied?

Free electrons drift towards the positive terminal of the battery, creating a net movement of charges which constitutes the electric current. Signup and view all the answers

Explain the condition under which no electric current flows in a copper wire according to Figure 2.1.

No electric current flows when the ends A and B of the copper wire are at the same electric potential. Signup and view all the answers

How does the analogy between water flow and electric current help in understanding electric potential?

The analogy shows that just as water flows from high to low gravitational potential, electric charges move from high to low electric potential, helping to understand the flow of current. Signup and view all the answers

Describe how the motion of electrons changes in a conductor when an electric field is applied.

When an electric field is applied, the electrons, despite their random zigzag motion due to collisions with ions, slowly drift along the conductor in a direction opposite to the electric field. Signup and view all the answers

Explain why there is no net flow of electrons in a conductor with no electric field.

In the absence of an electric field, electrons move randomly in all directions, and the number of electrons moving in each direction is balanced by those moving in the opposite direction, resulting in no net flow. Signup and view all the answers

What role do positive ions play in the generation of electric current in a conductor?

Positive ions do not move freely and thus do not directly contribute to the generation of electric current; they mostly collide with free electrons, causing resistance. Signup and view all the answers

What is drift velocity and how is it related to the applied electric field?

Drift velocity is the average velocity acquired by electrons in a conductor due to an applied electric field, and it is the net velocity in the direction opposite to the field. Signup and view all the answers

Why do electrons exhibit zigzag motion in a conductor even when an electric field is applied?

Electrons exhibit zigzag motion because they are constantly colliding with positive ions within the conductor, which frequently changes their direction of motion. Signup and view all the answers

How does the presence of an electric field cause a potential difference across a conductor?

An electric field is established by connecting a battery, causing a force on electrons that induces movement, creating a potential difference since electrons accumulate near one end and deplete from the other. Signup and view all the answers

Explain the relationship between instantaneous current and average current in terms of charge flow and time interval.

Instantaneous current is the limit of the average current as the time interval approaches zero, represented as $I = rac{dQ}{dt}$. Signup and view all the answers

What is the SI unit of electric current and how is it defined?

The SI unit of electric current is the ampere (A), defined as 1 coulomb of charge passing through a cross section of a conductor in 1 second. Signup and view all the answers

How does the conventional current direction relate to the actual flow of electrons in a typical circuit?

The conventional current flows from the positive terminal to the negative terminal, while electrons flow from the negative terminal to the positive terminal. Signup and view all the answers

If a charge of 150 C passes through a cross-section of a conductor in 30 seconds, calculate the average current.

The average current is 5 A. Signup and view all the answers

Define electric current as a scalar quantity and explain why it can be considered as such despite having direction.

Electric current is a scalar quantity because it is defined by the magnitude of charge flow per unit time, not by direction. Signup and view all the answers

Derive the expression for instantaneous current in terms of rate of change of charge.

Instantaneous current is derived as $I = rac{dQ}{dt}$ by taking the limit of average current as the time interval approaches zero. Signup and view all the answers

What is meant by the term 'conventional current,' and how does it differ from the actual particle flow in conductors?

Conventional current refers to the hypothetical flow of positive charges from the positive to the negative terminal, differing from the actual electron flow from negative to positive. Signup and view all the answers

How would the current change if the time for a charge of 120 C to pass through a conductor is reduced from 60 seconds to 30 seconds?

The current would double, becoming 4 A. Signup and view all the answers

Derive the expression for acceleration experienced by an electron in an electric field E using the given parameters.

a = eE/m Signup and view all the answers

Given an electric field magnitude of 570 NC^-1, calculate the force experienced by an electron.

F = 570 × 1.6 × 10^-19 N Signup and view all the answers

Explain why electrons in a conducting wire start moving as soon as a battery is connected, despite their low drift velocity.

The electric field propagates through the wire at the speed of light, causing immediate movement. Signup and view all the answers

What is the formula for the drift velocity (vd) of an electron in the presence of an electric field (E) and mean free time (τ)?

vd = -eEτ/m Signup and view all the answers

Define mobility (µ) of an electron and provide its formula.

Mobility is the magnitude of the drift velocity per unit electric field. µ = eτ/m Signup and view all the answers

Calculate the acceleration experienced by an electron in a copper wire when subjected to an electric field of 570 N/C.

1.001 × 10^14 m/s^2 Signup and view all the answers

Why is it incorrect to say 'charging the battery in my mobile' or 'my mobile phone battery has no charge'?

These phrases are incorrect because the battery's function is to provide potential difference, not to supply charge directly. Signup and view all the answers

What is the SI unit of electron mobility?

m^2V^-1s^-1 Signup and view all the answers

What is the current flowing through a 24 Ω resistor if the potential difference across it is 12 V?

0.5 A Signup and view all the answers

If the resistance of a conductor is 12 Ω and the conductivity of the material is $\frac{1}{480} Ω^{-1} m^{-1}$, what is the length of the conductor if its cross-sectional area is 4 $m^2$?

48 m Signup and view all the answers

How does the resistivity of a material affect its classification as a conductor, semiconductor, or insulator?

Conductors have the lowest resistivity, semiconductors have intermediate resistivity, and insulators have the highest resistivity. Signup and view all the answers

What is the resistivity of a material in which the resistance of a 1 m length and 1 m² cross-sectional area is 5 Ω?

5 Ω m Signup and view all the answers

Using equations (2.18) and (2.19), express resistance $R$ in terms of resistivity $ρ$ and the conductor's dimensions.

$R = \frac{ρl}{A}$ Signup and view all the answers

Calculate the resistance of a 2 m length copper wire with a cross-sectional area of $10^{-6} m^2$ if the resistivity of copper is $1.7 \times 10^{-8} Ω m$.

0.034 Ω Signup and view all the answers

A germanium semiconductor has a resistivity of 0.46 Ω m. What is the resistance of a germanium rod of length 0.5 m and cross-sectional area $5 \times 10^{-4} m^2$?

460 Ω Signup and view all the answers

Why is the SI unit of resistivity expressed as Ω m and what physical meaning does it convey?

Ω m represents the resistance of a material with a unit length and unit cross-sectional area. Signup and view all the answers

What is the equation relating the potential difference across a wire to the electric field and length of the wire?

V = El Signup and view all the answers

Write the expression for current density in terms of conductivity, voltage, and length.

J = σV/l Signup and view all the answers

How can the equation J = σΕ be rewritten in terms of current (I) and cross-sectional area (A)?

I/A = σV/l Signup and view all the answers

Explain how the resistance (R) of a conductor is expressed using length (l), conductivity (σ), and cross-sectional area (A).

R = l/σA Signup and view all the answers

According to Ohm's law, what is the relationship between potential difference, current, and resistance?

V = IR Signup and view all the answers

If a conductor has a resistance R, what is the formula to find resistance using potential difference and current?

R = V/I Signup and view all the answers

What is the SI unit of resistance and what does it signify in the context of Ohm's law?

Ohm (Ω) Signup and view all the answers

Describe the difference between ohmic and non-ohmic materials in terms of their I-V characteristics.

Ohmic materials have a linear I-V relationship; non-ohmic materials have a non-linear I-V relationship. Signup and view all the answers

What is the new resistance of a wire stretched uniformly to 8 times its original length if the original resistance was 20 Ω?

1280 Ω Signup and view all the answers

Why does stretching a wire increase its resistance, even though its volume remains the same?

The length increases and the cross-sectional area decreases. Signup and view all the answers

If the cross-sectional area of a wire decreases by a factor of 8 upon stretching, by what factor does the resistance increase?

64 Signup and view all the answers

For a rectangular block of metal, if a potential difference V is applied between faces A and B, what is the expression for resistance $R_{AB}$?

$R_{AB} = \frac{\rho C}{A B}$ Signup and view all the answers

Given a potential difference V across faces A and B of a rectangular block, how is the current $I_{AB}$ related to the resistance $R_{AB}$?

$I_{AB} = \frac{V}{R_{AB}} = \frac{V AB}{\rho C}$ Signup and view all the answers

When the same potential difference V is applied between faces B and C of the rectangular block, what is the new expression for $I_{BC}$ in terms of $I_{AB}$?

$I_{BC} = \frac{C^2}{A^2} I_{AB}$ Signup and view all the answers

Why is the current $I_{BC}$ greater than $I_{AB}$ for the same potential difference applied to the block of metal?

Because $C > A$ Signup and view all the answers

What are the resistance values of the human body in dry and wet conditions?

Dry skin: around 500 kΩ, Wet skin: around 1000 Ω Signup and view all the answers

Derive the relationship between current (I) and current density (J) for a conductor of cross-sectional area A.

I = JA Signup and view all the answers

Explain why the equation J = nevd is valid only when the current is perpendicular to the area A.

Because current density is defined as a vector whose direction is normal to the surface area it passes through. Signup and view all the answers

What is the significance of the equation J = σE in terms of Ohm's law?

It represents the microscopic form of Ohm's law. Signup and view all the answers

In the derivation of current I = neAvd, explain the relevance of the term ne and how it relates to the physical properties of the conductor.

The term ne represents the number of charge carriers (electrons) per unit volume in the conductor. Signup and view all the answers

Using the equation J = ne²τ/m E, derive the expression for conductivity (σ) in terms of n, e, τ, and m.

σ = ne²τ/m Signup and view all the answers

Describe the physical meaning of drift velocity (vd) and how it affects the current in a conductor.

Drift velocity (vd) is the average velocity of electrons moving through a conductor due to an electric field. Signup and view all the answers

Given the relationship J = nevd, how would doubling the electron density (n) affect the current density (J) for a given drift velocity (vd)?

Doubling the electron density (n) would double the current density (J). Signup and view all the answers

If the cross-sectional area A of a conductor is halved while keeping the current (I) constant, what happens to the current density (J)?

The current density (J) would double. Signup and view all the answers

Explain why the current remains the same across all resistors when they are connected in series?

The current remains the same across all resistors in series because the electric charges have only one path to follow, causing the same amount of charge to pass through each resistor. Signup and view all the answers

Using Ohm's Law, derive the expression for the equivalent resistance Rs in a series circuit with three resistors R1, R2, and R3.

By Ohm's Law, V = I(R1 + R2 + R3), and using equivalent resistance Rs, V = IRs. Thus, Rs = R1 + R2 + R3. Signup and view all the answers

If the supply voltage in a series circuit with three resistors is 24V, and the current through the resistors is 2A, find the total resistance Rs of the circuit.

Rs = V / I = 24V / 2A = 12Ω. Signup and view all the answers

In a series circuit with R1 = 4Ω, R2 = 6Ω, and R3 = 8Ω, calculate the total voltage if the current is 2A.

V = I(R1 + R2 + R3) = 2A(4Ω + 6Ω + 8Ω) = 2A * 18Ω = 36V. Signup and view all the answers

Given three resistors R1, R2, and R3 with values 5Ω each, calculate the equivalent resistance in series.

Rs = R1 + R2 + R3 = 5Ω + 5Ω + 5Ω = 15Ω. Signup and view all the answers

Why is the potential difference different across each resistor in a series circuit?

The potential difference is different across each resistor because each resistor has a different resistance value, causing different voltage drops according to Ohm's Law (V = IR). Signup and view all the answers

How does the total resistance of a series circuit compare to the individual resistances of the resistors in that circuit?

The total resistance of a series circuit is always greater than each of the individual resistances. Signup and view all the answers

If the supply voltage is shared among three resistors in series as V1, V2, and V3, write a formula that relates the supply voltage V and the potential differences across the three resistors.

V = V1 + V2 + V3. Signup and view all the answers

Study Notes