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Questions and Answers
What is the average value of the time interval ti for the electrons after many collisions?
What happens to the velocity of an electron immediately after a collision?
What role does the electric field play in the movement of electrons in this scenario?
What does the symbol τ represent in the context of the average velocity equation?
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How is the average velocity of electrons expressed based on the equation provided?
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Which equation best describes the effect of relaxation time on the average velocity of the electrons?
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What is the underlying assumption made about the time intervals of the collisions between electrons?
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What is the implication of having an average initial velocity (vi) equal to zero for the electrons?
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What does the potential difference V between the positive terminal P and the negative terminal N represent?
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According to the junction rule, what must be true at any junction in an electrical circuit?
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What could happen if the currents entering a junction did not equal the currents leaving?
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What does the loop rule state about the potential changes in a closed loop?
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For a cell with an internal resistance r, how is the potential difference V expressed if current I flows from P to N?
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What is the requirement for currents in a steady state at a junction?
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What is an implication of the loop rule when analyzing circuits?
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In a simple closed circuit with one cell and one resistor, what maintains a constant potential difference?
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What is the purpose of Kirchhoff's rules in electric circuit analysis?
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What are the dimensions of electric current in the SI system?
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What unit is used to measure electric voltage?
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If two cells are connected with their positive terminals tied together, what happens to the currents flowing from the terminals?
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Which equation correctly represents the internal resistance of multiple cells connected in parallel?
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Which of the following correctly indicates the relationship defined by Ohm's Law?
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What is the dimension of resistivity?
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How is the equivalent EMF of cells connected in parallel calculated?
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What indicates the direction of current flow in a resistor when labeling it?
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How is electrical conductivity related to resistivity?
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What is the unit of current density?
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What occurs when the determined current in a resistor is negative?
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What happens to the equivalent internal resistance when adding more cells in parallel?
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What does the symbol 'I' represent in electrical terms?
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What is the relationship between drift speed and electric field in terms of mobility?
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What was Kirchhoff mainly known for in addition to his contributions to circuits?
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What does the term electromotive force (emf) primarily refer to?
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According to Ohm's law, how does current relate to voltage?
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Which equation correctly expresses the relationship of resistance to length and cross-sectional area?
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Which materials are likely to exhibit the lowest electrical resistivity?
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What does the drift velocity (vd) of charge carriers relate to?
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What denotes the number density (n) of charge carriers?
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In what scenario can current flow be carried by both positive and negative ions?
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If the current density (j) is constant over a cross-sectional area, what is true about the current (I) through that area?
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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.