Electric Fields and Kirchhoff's Rules

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Questions and Answers

What is the average value of the time interval ti for the electrons after many collisions?

It is less than the total time t.

It is greater than the total time t.

It varies randomly for each electron.

It is equal to the total time t. (correct)

What happens to the velocity of an electron immediately after a collision?

It becomes constant.

It is determined by the electric field only.

It is completely random in direction. (correct)

It decreases significantly.

What role does the electric field play in the movement of electrons in this scenario?

It causes them to drift slightly in the opposite direction. (correct)

It has no effect on their velocity.

It increases their average velocity significantly.

It decelerates the electrons.

What does the symbol τ represent in the context of the average velocity equation?

The relaxation time. Signup and view all the answers

How is the average velocity of electrons expressed based on the equation provided?

It equals the initial velocity subtracted by the product of relaxation time and electric field. Signup and view all the answers

Which equation best describes the effect of relaxation time on the average velocity of the electrons?

v_d = 0 - (eE/m)τ Signup and view all the answers

What is the underlying assumption made about the time intervals of the collisions between electrons?

They vary randomly among electrons. Signup and view all the answers

What is the implication of having an average initial velocity (vi) equal to zero for the electrons?

They randomly change direction after collisions. Signup and view all the answers

What does the potential difference V between the positive terminal P and the negative terminal N represent?

The difference in electric potential energy per unit charge Signup and view all the answers

According to the junction rule, what must be true at any junction in an electrical circuit?

The sum of currents entering equals the sum of currents leaving Signup and view all the answers

What could happen if the currents entering a junction did not equal the currents leaving?

Charge would accumulate at the junction Signup and view all the answers

What does the loop rule state about the potential changes in a closed loop?

The algebraic sum of changes in potential is zero Signup and view all the answers

For a cell with an internal resistance r, how is the potential difference V expressed if current I flows from P to N?

V = e - Ir Signup and view all the answers

What is the requirement for currents in a steady state at a junction?

There must be no accumulation of charge Signup and view all the answers

What is an implication of the loop rule when analyzing circuits?

Potential differences in cells influence total voltage Signup and view all the answers

In a simple closed circuit with one cell and one resistor, what maintains a constant potential difference?

The electric field in the circuit Signup and view all the answers

What is the purpose of Kirchhoff's rules in electric circuit analysis?

To analyze complex circuits with multiple resistors and cells Signup and view all the answers

What are the dimensions of electric current in the SI system?

[A] Signup and view all the answers

What unit is used to measure electric voltage?

V Signup and view all the answers

If two cells are connected with their positive terminals tied together, what happens to the currents flowing from the terminals?

The currents will flow from the positive terminals Signup and view all the answers

Which equation correctly represents the internal resistance of multiple cells connected in parallel?

$\frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2} + \cdots + \frac{1}{r_n}$ Signup and view all the answers

Which of the following correctly indicates the relationship defined by Ohm's Law?

V = IR Signup and view all the answers

What is the dimension of resistivity?

[M L3 T –3 A–2] Signup and view all the answers

How is the equivalent EMF of cells connected in parallel calculated?

$\epsilon_{eq} = \frac{\epsilon_1}{r_{1}} + \frac{\epsilon_2}{r_{2}} + \cdots + \frac{\epsilon_n}{r_{n}}$ Signup and view all the answers

What indicates the direction of current flow in a resistor when labeling it?

An arrow placed next to the current symbol Signup and view all the answers

How is electrical conductivity related to resistivity?

s = 1/r Signup and view all the answers

What is the unit of current density?

A m–2 Signup and view all the answers

What occurs when the determined current in a resistor is negative?

The current flows in the opposite direction to the arrow Signup and view all the answers

What happens to the equivalent internal resistance when adding more cells in parallel?

It decreases Signup and view all the answers

What does the symbol 'I' represent in electrical terms?

Electric current Signup and view all the answers

What is the relationship between drift speed and electric field in terms of mobility?

vd = mE Signup and view all the answers

What was Kirchhoff mainly known for in addition to his contributions to circuits?

Spectroscopy Signup and view all the answers

What does the term electromotive force (emf) primarily refer to?

The work done per unit charge by a source Signup and view all the answers

According to Ohm's law, how does current relate to voltage?

Current is directly proportional to voltage Signup and view all the answers

Which equation correctly expresses the relationship of resistance to length and cross-sectional area?

R = ρl/A Signup and view all the answers

Which materials are likely to exhibit the lowest electrical resistivity?

Metals such as copper and silver Signup and view all the answers

What does the drift velocity (vd) of charge carriers relate to?

The speed at which charge carriers move through a material Signup and view all the answers

What denotes the number density (n) of charge carriers?

The number of charge carriers per unit volume Signup and view all the answers

In what scenario can current flow be carried by both positive and negative ions?

In electrolytic liquids and ionic crystals Signup and view all the answers

If the current density (j) is constant over a cross-sectional area, what is true about the current (I) through that area?

It is equal to nevd A Signup and view all the answers

Study Notes

Electron Movement in an Electric Field

The velocity of an electron after the last collision (vi) is given by the equation: Vi = vi + (-eE/m)ti, where e is the charge of an electron, E is the electric field strength, m is the mass of the electron, and ti is the time interval since the last collision.
The average velocity of electrons (vd) is calculated by averaging the velocities of all electrons at a given time.
Since electron collisions occur randomly and not at regular intervals, the average time between collisions (τ) is introduced, which is known as the relaxation time.
The average velocity of electrons (vd) can be expressed as: vd = -eEτ/m.

Kirchhoff's Rules

Kirchhoff's rules are essential for analyzing complex electric circuits.
Junction Rule: The sum of currents entering a junction equals the sum of currents leaving the junction. This rule ensures charge conservation at junctions.
Loop Rule: The algebraic sum of potential changes around any closed loop in a circuit is zero. This rule reflects the conservative nature of electrostatic forces.

Electromotive Force (emf)

The emf is the work done per unit charge by a source in moving charges from a lower to higher potential.
This work is done by an external agency within the source, making it a non-conservative force.
The emf is not a force but rather a voltage difference between the terminals of a source in an open circuit.

Resistance and Resistivity

Resistance (R) is a measure of a material's opposition to current flow. It's directly proportional to the material's length (l) and inversely proportional to its cross-sectional area (A).
Resistivity (ρ) is an intrinsic property of the material, independent of its dimensions, and reflects its ability to conduct electricity. Lower resistivity indicates better conductivity.
The relationship between resistance and resistivity is: R = ρl/A

Conductivity

The conductivity (σ) of a material is the reciprocal of its resistivity. High conductivity indicates a material's ability to conduct electricity readily.
σ= 1/ρ

Current Density

Current density (j) represents the amount of charge flowing per unit time per unit area perpendicular to the flow.
j = nqvd, where n is the number density of charge carriers, q is the charge of each carrier, and vd is the drift velocity of the charge carriers.

Physical Quantities and their Units

Electric current (I): Measured in Amperes (A)
Charge (Q, q): Measured in Coulombs (C)
Voltage (V), Electric Potential Difference: Measured in Volts (V)
Electromotive force (e): Measured in Volts (V)
Resistance (R): Measured in Ohms (Ω)
Resistivity (ρ): Measured in Ohm-meters (Ωm)
Conductivity (σ): Measured in Siemens per meter (S/m)
Electric field (E): Measured in Volts per meter (V/m)
Drift Speed (vd): Measured in meters per second (m/s)
Relaxation Time (τ): Measured in seconds (s)
Current Density (j): Measured in Amperes per square meter (A/m²)
Mobility (μ): Measured in square meters per volt per second (m²/Vs)

Points To Ponder

Current is a scalar quantity despite being represented by arrows. Currents do not add vectorially.

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Description

Explore the principles of electron movement in electric fields and Kirchhoff's rules for circuit analysis. This quiz tests your understanding of concepts like velocity of electrons, relaxation time, and current conservation at junctions. Perfect for students studying electricity.