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, its direction, units, and fundamental laws like Kirchhoff’s laws.

Key Terms and Concepts:

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

• Conventional current direction: Defined as the direction positive charges would flow (from higher to lower potential).

• Kirchhoff’s junction law: States that the total current entering a junction equals the total current leaving (conservation of charge).

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

Step-by-Step Guidance

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

2. For each statement, ask yourself: Is this consistent with the standard physics definitions and laws?

3. Pay special attention to the direction of electron flow versus conventional current, and the meaning of Kirchhoff’s laws.

4. Identify which statement contradicts the established concepts above.

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 and how each variable affects $R$.

2. Analyze each statement: What happens to $R$ if $\rho$, $L$, or $A$ increases?

3. Check if any statement contradicts the formula above.

4. Determine which statement is consistent with the formula and which are not.

Try solving on your own before revealing the answer!

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:

• EMF ($\mathcal{E}$): The voltage provided by a battery.

• Ideal wires: No voltage drop across them.

• Potential drops: Occur across resistors, not ideal wires.

Step-by-Step Guidance

1. Assign $V = 0$ at the negative terminal of the lower battery as instructed.

2. Move through the circuit, adding/subtracting potential as you cross batteries and the resistor.

3. At each labeled point ($A, B, C, D, E$), calculate the potential relative to the reference point.

4. Rank the potentials from highest to lowest based on your analysis.

Try solving on your own before revealing the answer!

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 Ohmic/Non-Ohmic Behavior

This question tests your understanding of Ohm’s law and how to interpret $I$ vs. $\Delta V$ graphs.

Key Concepts:

• Ohm’s Law: $V = IR$

• Ohmic behavior: Linear $I$ vs. $V$ relationship (constant resistance).

• Non-ohmic behavior: Nonlinear $I$ vs. $V$ relationship (resistance changes with $V$).

Step-by-Step Guidance

1. Examine the graph: Is the $I$ vs. $\Delta V$ relationship linear everywhere?

2. Recall that the slope of the $I$ vs. $V$ graph gives $1/R$ for ohmic conductors.

3. Determine if Ohm’s law applies throughout the entire range or only part of it.

4. Match the correct statement to your observations.

Try solving on your own before revealing the answer!

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 heat produced in a resistor.

Key Formulas:

$R = \rho \frac{L}{A}$ $A = \pi R^2$ $P = \frac{V^2}{R}$

• $P$ = power (rate of heat generation)

• $V$ = voltage across resistor

Step-by-Step Guidance

1. Calculate the new length and radius: $L_{new} = 2L$, $R_{new} = 2R$.

2. Find the new cross-sectional area: $A_{new} = \pi (2R)^2$.

3. Substitute the new values into the resistance formula to find $R_{new}$.

4. Use the power formula to determine how the heat generation changes with the new resistance.

Try solving on your own before revealing the answer!

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 basic circuit rules.

Key Concepts:

• Parallel connection: Components share the same potential difference.

• Series connection: Same current flows through components.

• Junction rule: Total current splits at a junction.

Step-by-Step Guidance

1. Analyze the circuit diagram to identify which resistors are in series or parallel.

2. Check if the statements about current and potential difference match the circuit configuration.

3. Determine which statement does not fit with the circuit analysis.

4. Recall the definitions of series and parallel connections to help your reasoning.

Try solving on your own before revealing the answer!

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 Formula:

$Q(t) = CV (1 - e^{-t/\tau})$ $\tau = RC$

• $Q(t)$ = charge on capacitor at time $t$

• $C$ = capacitance

• $V$ = battery voltage

• $\tau$ = time constant

Step-by-Step Guidance

1. Recall the meaning of the time constant $\tau$ in an RC circuit.

2. Evaluate each statement using the formula for $Q(t)$ at $t = 0$ and $t = \tau$.

3. Check if $\tau = R/C$ or $\tau = RC$.

4. Determine which statement is consistent with the formula and the physical meaning of $\tau$.

Try solving on your own before revealing the answer!

Q8. Given the equations for 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.

Key Concepts:

• Junction Rule: Conservation of charge at a node.

• Loop Rule: Conservation of energy around a closed loop.

• Current direction: Negative value means actual 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 interpretation of negative current values.

3. Analyze the statements about potential differences across resistors.

4. Determine which statement is inconsistent with the rules or the given values.

Try solving on your own before revealing the answer!

Q9. Three particles travel through a region with a magnetic field 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:

• Right-hand rule: For positive charges, thumb = velocity, fingers = field, palm = force direction.

• Neutral particles: Not affected by magnetic fields.

• Negative charges: Force direction is opposite to right-hand rule.

Step-by-Step Guidance

1. Observe the paths of the particles in the diagram (if provided).

2. Apply the right-hand rule to determine the force direction for each particle.

3. Identify which particle is unaffected (neutral), and which are positive or negative based on their deflection.

4. Match the observed behavior to the correct charge assignments.

Try solving on your own before revealing the answer!

Q10. For a horseshoe magnet 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).

Key Formula:

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

• $\vec{F}$ = force on the wire

• $I$ = current

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

• $\vec{B}$ = magnetic field

Step-by-Step Guidance

1. Determine the direction of the current in the wire when the switch is closed.

2. Identify the direction of the magnetic field (from north to south pole).

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

4. Choose the answer that matches the force direction you found.

Try solving on your own before revealing the answer!

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.

Step-by-Step Guidance

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

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

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

Try solving on your own before revealing the answer!

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 in bar magnets.

Key Concepts:

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

• Cutting a magnet creates two smaller magnets, each with both poles.

Step-by-Step Guidance

1. Recall what happens to the poles when a bar magnet is cut in half.

2. Decide if the left piece will have only a south pole or both poles.

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

Try solving on your own before revealing the answer!

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 basis for Kirchhoff’s junction rule.

Key Concepts:

• Junction rule: Conservation of charge.

• Loop rule: Conservation of energy.

Step-by-Step Guidance

1. Recall which physical law underlies the junction rule.

2. Decide if the statement is true or false based on your knowledge.

Try solving on your own before revealing the answer!

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 is distributed among capacitors in parallel.

Key Formula:

$Q = CV$

• In parallel, each capacitor has the same voltage across it.

• Charge stored depends on each capacitor’s capacitance.

Step-by-Step Guidance

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

2. Consider if 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 your reasoning.

Try solving on your own before revealing the answer!

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 on moving charges.

Key Concepts:

• Magnetic force is always perpendicular to velocity.

• Work is done only by forces with a component along the direction of motion.

Step-by-Step Guidance

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

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

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

Try solving on your own before revealing the answer!