PHYS 113 - Introduction to Physics II: Review 3 – Step-by-Step Study Guidance

Q1. Which of the following statements about electric current is NOT correct?

Background

Topic: Electric Current and Circuit Concepts

This question tests your understanding of the definition of electric current, conventional current direction, the unit of current, and Kirchhoff’s laws.

Key Terms and Concepts:

• Electric current: The flow of electric charge, typically measured in amperes (A).

• Conventional current: Direction is defined as the flow of positive charge (from higher to lower potential).

• Kirchhoff’s junction law: Based on conservation of charge.

• Unit: $1\ \mathrm{A} = 1\ \mathrm{C/s}$

Step-by-Step Guidance

1. Read each statement carefully and recall the definitions and laws related to electric current.

2. For statement (a), remember the conventional direction of current and how it relates to potential difference.

3. For statement (b), consider the actual movement of electrons versus the conventional current direction in typical circuits.

4. For statement (c), recall what Kirchhoff’s junction law states and its physical basis.

5. For statement (d), check the SI unit for current and its relation to charge and time.

Try solving on your own before revealing the answer!

Q2. Which of the following statements about a wire resistor with resistivity $\rho$, length $L$, and cross-sectional area $A$ is true?

Background

Topic: Resistance and Resistivity

This question tests your understanding of how resistance depends on material properties and geometry.

Key Formula:

$R = \rho \frac{L}{A}$

• $R$ = resistance (ohms, $\Omega$)

• $\rho$ = resistivity (ohm-meters, $\Omega \cdot m$)

• $L$ = length (meters)

• $A$ = cross-sectional area ($m^2$)

Step-by-Step Guidance

1. Recall the formula for resistance in terms of resistivity, length, and area.

2. Analyze how resistance changes if $\rho$, $L$, or $A$ are increased, one at a time.

3. Check each statement (a)-(c) against the formula to see if it matches the physical relationship.

4. Consider if any of the statements are correct, or if 'none of the above' is the best choice.

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Q3. Two identical batteries with emf $\mathcal{E}$ are connected in series with a single resistor. What is the correct ranking of the electric potentials $V_A, V_B, V_C, V_D, V_E$ from highest to lowest, assuming ideal wires?

Background

Topic: Electric Potential in Circuits

This question tests your ability to analyze potential differences in a series circuit with batteries and a resistor.

Key Concepts:

• In ideal wires, there is no voltage drop.

• Potential increases across a battery (from negative to positive terminal).

• Potential drops across a resistor (in the direction of current).

Step-by-Step Guidance

1. Identify the path of current and label the potentials at each point (A, B, C, D, E) based on the circuit diagram.

2. Recall that the potential increases by $\mathcal{E}$ across each battery (from - to + terminal).

3. Determine where the largest potential is (relative to the defined zero point at the negative terminal of the lower battery).

4. Consider the potential drops across the resistor and how the potentials at each labeled point compare.

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Q4. The graph shows the current vs. potential difference for a conductor with non-zero resistance. Which statement is true?

Background

Topic: Ohm's Law and Non-Ohmic Conductors

This question tests your understanding of ohmic vs. non-ohmic behavior and how to interpret $I$ vs. $\Delta V$ graphs.

Key Concepts:

• Ohm's Law: $V = IR$ (linear relationship for ohmic conductors)

• For ohmic conductors, the $I$ vs. $V$ graph is a straight line.

• The slope of the $I$ vs. $V$ graph gives information about resistance.

Step-by-Step Guidance

1. Examine the graph and identify if the relationship is linear or has different regions.

2. Recall what it means for a conductor to be ohmic (constant resistance, linear graph).

3. Determine what the slope of the straight-line segment represents.

4. Consider whether Ohm's law applies in all regions of the graph or only in certain segments.

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Q5. A cylindrical wire resistor with radius $R$ and length $L$ is connected to a battery with emf $\mathcal{E}$, generating heat. If both the radius and length are increased by a factor of 2, which statement correctly describes the change in resistance and heat?

Background

Topic: Resistance, Power, and Heat Generation in Resistors

This question tests your understanding of how geometric changes affect resistance and the heat generated in a resistor.

Key Formulas:

• Resistance: $R = \rho \frac{L}{A}$, where $A = \pi R^2$

• Power (heat generated): $P = \frac{V^2}{R}$

Step-by-Step Guidance

1. Calculate the new length and radius: $L' = 2L$, $R' = 2R$.

2. Find the new cross-sectional area: $A' = \pi (2R)^2 = 4\pi R^2$.

3. Substitute the new values into the resistance formula to find the new resistance $R'$.

4. Use the new resistance to analyze how the heat generated (power) changes, using $P = \frac{V^2}{R}$.

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Q6. Consider the circuit below. Which of the following statements is NOT true?

Background

Topic: Series and Parallel Circuits

This question tests your ability to identify series and parallel relationships and apply current and voltage rules in circuits.

Key Concepts:

• In parallel, voltage across components is the same; in series, current is the same.

• Total current at a junction: $I = I_1 + I_2$ (Kirchhoff's junction law)

Step-by-Step Guidance

1. Identify which resistors are in series and which are in parallel by tracing the circuit.

2. Check if the total current splits at a junction and if the voltage across certain points is the same.

3. Analyze each statement (a)-(d) to see if it matches the circuit configuration.

4. Determine which statement does not fit with the rules for series and parallel circuits.

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Q7. A resistor $R$ and a capacitor $C$ are connected in series to a battery $V$. If a switch is closed at $t = 0$, the charge stored in the capacitor as a function of time is $Q(t) = CV (1 - e^{-t/\tau})$. Which statement is true?

Background

Topic: RC Circuits and Time Constant

This question tests your understanding of charging a capacitor in an RC circuit and the meaning of the time constant $\tau$.

Key Terms and Formulas:

• Time constant: $\tau = RC$

• Maximum charge: $Q_{max} = CV$

• Charging equation: $Q(t) = CV (1 - e^{-t/\tau})$

Step-by-Step Guidance

1. Recall the definition of the time constant $\tau$ for an RC circuit.

2. Analyze the charging equation at $t = 0$ and as $t \to \infty$.

3. Check what fraction of the maximum charge is stored at $t = \tau$.

4. Evaluate each statement (a)-(d) based on the above analysis.

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Q8. Given the following Kirchhoff’s rules and $R_1 = R_2 = R_3 = 100\ \Omega$, which statement is NOT true?

Background

Topic: Kirchhoff’s Rules for Circuits

This question tests your understanding of the application of Kirchhoff’s junction and loop rules, and the interpretation of current directions and potential differences.

Key Concepts:

• Junction rule: Conservation of charge at a node.

• Loop rule: Sum of potential differences around a closed loop is zero (conservation of energy).

• Sign of current: Negative value indicates direction is opposite to assumed.

Step-by-Step Guidance

1. Identify which equations correspond to the junction rule and which to the loop rule.

2. Check the meaning of the sign of the current values given.

3. Analyze the potential differences across $R_2$ and $R_3$ based on the circuit configuration.

4. Evaluate each statement (a)-(d) for correctness based on the above analysis.

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Q9. Three particles travel through a region of space where the magnetic field is out of the page. What are the signs of the charges of these three particles?

Background

Topic: Magnetic Force on Moving Charges

This question tests your understanding of the right-hand rule and how charged particles move in a magnetic field.

Key Concepts:

• Magnetic force: $\vec{F} = q\vec{v} \times \vec{B}$

• Right-hand rule: Determines direction of force for positive charges; reverse for negative charges.

• Neutral particles are unaffected by magnetic fields.

Step-by-Step Guidance

1. For each particle, observe its path (straight, curved left, curved right) in the magnetic field.

2. Apply the right-hand rule to determine the sign of the charge based on the direction of deflection.

3. Identify which particle is neutral (no deflection).

4. Match the observed behavior to the possible charge combinations.

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Q10. For the horseshoe magnet shown, with the left end as north and right end as south, when the switch is closed, which way will the wire between the poles initially deflect?

Background

Topic: Magnetic Force on a Current-Carrying Wire

This question tests your understanding of the force on a wire in a magnetic field (motor effect) and the right-hand rule.

Key Formula:

$\vec{F} = I \vec{L} \times \vec{B}$

• $I$ = current

• $\vec{L}$ = length vector in direction of current

• $\vec{B}$ = magnetic field

Step-by-Step Guidance

1. Determine the direction of the magnetic field (from north to south pole).

2. Identify the direction of current in the wire when the switch is closed.

3. Apply the right-hand rule to find the direction of the force on the wire.

4. Match the direction of force to the possible answer choices (right, left, up, down).

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Q11. A charged particle moving in a static uniform magnetic field may experience a magnetic force, but its speed will not change: True or False?

Background

Topic: Magnetic Forces and Particle Motion

This question tests your understanding of how magnetic forces affect the motion (speed and direction) of charged particles.

Key Concepts:

• Magnetic force is always perpendicular to velocity.

• Perpendicular force changes direction, not speed (circular motion).

Step-by-Step Guidance

1. Recall the direction of the magnetic force relative to the velocity of the particle.

2. Consider whether a perpendicular force can change the speed of a particle.

3. Think about the type of motion (e.g., circular) that results from this force.

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Q12. If you cut a straight bar magnet in half (with the south pole on the left and the north pole on the right), the left piece will have a south pole on its left end and a north pole on its right end: True or False?

Background

Topic: Magnetic Poles and Magnetism

This question tests your understanding of the nature of magnetic poles and what happens when a magnet is divided.

Key Concepts:

• Every magnet has both a north and a south pole.

• Cutting a magnet creates two smaller magnets, each with a north and south pole.

Step-by-Step Guidance

1. Recall the basic property of magnetic dipoles.

2. Consider what happens to the poles when a magnet is cut in half.

3. Decide if the statement matches the physical reality of magnets.

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Q13. Kirchhoff’s junction rule follows from the conservation of energy: True or False?

Background

Topic: Kirchhoff’s Laws

This question tests your understanding of the physical principles underlying Kirchhoff’s junction and loop rules.

Key Concepts:

• Junction rule: Conservation of charge.

• Loop rule: Conservation of energy.

Step-by-Step Guidance

1. Recall what each of Kirchhoff’s rules represents physically.

2. Match the junction rule to the correct conservation law.

3. Decide if the statement is true or false based on your understanding.

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Q14. If capacitors are connected in parallel to a battery, they all store the same amount of charge: True or False?

Background

Topic: Capacitors in Circuits

This question tests your understanding of how charge and voltage are distributed among capacitors in parallel.

Key Concepts:

• In parallel, voltage across each capacitor is the same.

• Charge stored: $Q = CV$

• Capacitance may differ for each capacitor.

Step-by-Step Guidance

1. Recall how voltage and charge are distributed in parallel capacitor arrangements.

2. Consider whether all capacitors must have the same charge or if it depends on their capacitance.

3. Decide if the statement is true or false based on the formula $Q = CV$.

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Q15. An electron moving through a region of uniform magnetic field gains kinetic energy due to the magnetic force: True or False?

Background

Topic: Work Done by Magnetic Forces

This question tests your understanding of whether magnetic forces can do work and change the kinetic energy of a charged particle.

Key Concepts:

• Magnetic force is always perpendicular to velocity.

• Work done by a force: $W = \vec{F} \cdot \vec{d}$

• Perpendicular force does no work (no change in kinetic energy).

Step-by-Step Guidance

1. Recall the direction of the magnetic force relative to the velocity of the electron.

2. Consider whether a perpendicular force can do work on a particle.

3. Decide if the kinetic energy of the electron can change due to the magnetic force alone.

Try solving on your own before revealing the answer!