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, and related physical laws and units.

Key Terms and Concepts:

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

• Conventional current direction: From higher to lower electric potential (opposite to electron flow in most circuits).

• Kirchhoff’s junction law: Conservation of charge at a circuit junction.

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

Step-by-Step Guidance

1. Read each statement carefully and recall the definitions and conventions for electric current.

2. For each statement, ask yourself: Is this consistent with what you know about current direction, electron flow, Kirchhoff’s laws, and units?

3. Identify which statement contradicts the standard physics definitions or laws.

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 of a Conductor

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 how each variable in the formula affects resistance: increasing $\rho$, $L$, or $A$.

2. Analyze each statement in the question using the formula above.

3. Determine which statement correctly describes the relationship between resistance and the variables.

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 Series 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 (by $IR$).

Step-by-Step Guidance

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

2. Trace the circuit, adding or subtracting potential as you move through batteries and the resistor.

3. Rank the points $A, B, C, D, E$ based on the changes in potential as you move through the circuit.

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 Non-Ohmic Conductors

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

Key Concepts:

• Ohm’s law: $V = IR$ (linear relationship for ohmic conductors).

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

• Non-ohmic behavior: Nonlinear regions in the graph.

Step-by-Step Guidance

1. Examine the graph for linear and nonlinear regions.

2. Recall that for ohmic conductors, the $I$ vs. $V$ graph is a straight line through the origin.

3. Determine which statement correctly describes the behavior shown in the graph, especially around $\Delta V = V'$.

Try solving on your own before revealing the answer!

Q5. If both the radius and length of a cylindrical wire resistor are increased by a factor of 2, which statement correctly describes the change in resistance and heat generated?

Background

Topic: Resistance and Power Dissipation in Resistors

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

Key Formulas:

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

Step-by-Step Guidance

1. Calculate the new length and area after both are doubled.

2. Substitute the new values into the resistance formula to see how $R$ changes.

3. Use the power formula to determine how the heat generated changes with the new resistance.

Try solving on your own before revealing the answer!

Q6. Consider the circuit below. Which statement is NOT true?

Background

Topic: Series and Parallel Circuits

This question tests your ability to identify series and parallel relationships and apply Kirchhoff’s laws.

Key Concepts:

• Current in parallel branches: $I = I_1 + I_2$

• Potential difference across parallel elements is the same.

• Resistors in parallel and series: recognize configurations.

Step-by-Step Guidance

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

2. Check each statement against the circuit configuration and Kirchhoff’s laws.

3. Identify the statement that does not match the circuit’s properties.

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:

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

Step-by-Step Guidance

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

2. Analyze the behavior of $Q(t)$ at $t=0$ and as $t \to \infty$.

3. Check each statement for accuracy based on the formula and your understanding of capacitor charging.

Try solving on your own before revealing the answer!

Q8. Given the 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 interpreting current directions.

Key Concepts:

• Junction rule: Conservation of charge at a node.

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

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

Step-by-Step Guidance

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

2. Check the interpretation of current directions and potential differences across resistors.

3. Determine which statement does not accurately reflect the circuit analysis.

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 their charges?

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: Determines force direction for positive charges.

• Neutral particles are unaffected by magnetic fields.

• Negative charges experience force in the opposite direction to the right-hand rule.

Step-by-Step Guidance

1. For each particle, observe its path and use the right-hand rule to infer the sign of its charge.

2. Remember that a neutral particle will not be deflected by the magnetic field.

3. Match the observed behavior to the possible charge assignments.

Try solving on your own before revealing the answer!

Q10. For a wire between the poles of a horseshoe magnet (left: north, right: south), when the switch is closed, which way will the wire 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 (the motor effect).

Key Formula:

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

• Direction of force: Use the right-hand rule for current and magnetic field.

Step-by-Step Guidance

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

2. Use the right-hand rule to determine the direction of the force on the wire.

3. Relate the force direction to the possible answer choices (right, left, up, down).

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: Work Done by Magnetic Forces

This question tests your understanding of whether magnetic forces can change the speed (kinetic energy) of a charged particle.

Key Concepts:

• Magnetic force is always perpendicular to velocity.

• Work done by magnetic force: $W = 0$

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 the 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. Visualize what happens to the magnetic domains when a bar magnet is cut in half.

2. Decide if the left piece can have only a south pole on its left end and a north pole on its right end.

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

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 principle underlying Kirchhoff’s junction rule.

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. Determine whether the junction rule is based on conservation of energy or charge.

3. Decide if the statement is true or false.

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 Parallel

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

Key Formula:

$Q = CV$

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

• 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. Determine if all capacitors must store the same charge or if it depends on their capacitance.

3. Decide if the statement is true or false.

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 a charged particle.

Key Concepts:

• Magnetic force is always perpendicular to velocity.

• Work done by magnetic force: $W = 0$

• Kinetic energy changes only if work is done.

Step-by-Step Guidance

1. Recall the relationship between force, work, and kinetic energy.

2. Consider the direction of the magnetic force relative to the electron’s motion.

3. Decide if the electron’s kinetic energy can increase due to the magnetic force alone.

Try solving on your own before revealing the answer!