Physics II Exam 2 Study Guide: Capacitance, DC Circuits, and Current

Exam 2 Preparation Overview

This study guide summarizes the key concepts and problem types for a college-level Physics II exam covering Chapters 24, 25, and 26. The focus is on capacitance, DC circuits, current, resistance, and related problem-solving skills. Students are expected to recall foundational knowledge from earlier physics courses and apply it to new contexts.

General Exam Information

• Exam covers Chapters 24–26 (lectures 10–18).

• Closed book and closed notes; a 3x5 card with equations is allowed.

• Calculator required; no cell phones permitted.

• Exam consists of 4 multi-part problems, including conceptual and quantitative questions.

• All necessary constants and complex integrals will be provided within the problems.

Background Knowledge from Previous Courses

Mathematical and Physical Foundations

• Area and Volume Formulas: Know how to calculate the area and volume of circles, cylinders, and spheres.

• Newton's Laws: Understand the basic laws of motion and their application in 1D and 2D.

• Work and Energy: Be able to define work and potential energy, and relate them through the work-energy theorem.

• Calculus Skills: Differentiate and integrate polynomials, sine, and cosine functions.

• Quadratic Equations: Solve quadratic equations as they arise in physics problems.

Review of Prior Chapters

• Review notes from Chapters 21–23, especially sections relevant to Chapters 24–27.

• Basic knowledge of electric fields and electric potentials is assumed, particularly for constant electric fields.

• Note: There will be no Gauss' Law problems, but understanding the concepts is important.

Capacitance and Capacitors

Key Concepts

• Definition of Capacitance: Capacitance (C) is the ability of a system to store electric charge per unit potential difference. $C = \frac{Q}{V}$

• Parallel Plate Capacitor: For two parallel plates of area A separated by distance d in vacuum: $C = \varepsilon_0 \frac{A}{d}$

• Equivalent Capacitance:

  • Series: $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$

  • Parallel: $C_{eq} = C_1 + C_2 + \cdots$

• Energy Stored in a Capacitor: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$

• Dielectrics: Inserting a dielectric increases capacitance by a factor of the dielectric constant κ: $C = \kappa \varepsilon_0 \frac{A}{d}$

• Atomic Picture of Dielectrics: Dielectrics become polarized in an electric field, reducing the effective field and increasing capacitance.

Typical Exam Problems

• Calculate capacitance for various geometries (spherical, cylindrical, etc.).

• Analyze how Q (charge), V (voltage), C (capacitance), E (electric field), and U (energy) change with geometry or dielectric insertion.

• Distinguish between constant voltage (V) and constant charge (Q) scenarios when a dielectric is inserted.

• Describe capacitor behavior in DC circuits.

Current, Resistance, and Electromotive Force (EMF)

Key Concepts

• Current (I): The rate of flow of electric charge. $I = \frac{dQ}{dt}$

• Current Density (J): Current per unit area. $J = \frac{I}{A}$

• Resistance (R): Opposition to current flow. $R = \frac{V}{I}$

• Resistivity (ρ): Material property relating resistance to geometry. $R = \rho \frac{L}{A}$

• Ohm's Law: $V = IR$

• EMF (ε): The energy provided per unit charge by a source. For a source with internal resistance $r$: $V = \varepsilon - Ir$

• Electrical Power: $P = IV = I^2R = \frac{V^2}{R}$

• Atomic View: Current in a wire is due to the drift of electrons under an electric field.

Typical Exam Problems

• Calculate potential drops between points in a circuit.

• Determine power delivered and power loss in resistors.

• Analyze lightbulb behavior in circuits.

DC Circuits

Key Concepts

• Ohm's Law: Fundamental relationship between voltage, current, and resistance.

• Equivalent Resistance:

  • Series: $R_{eq} = R_1 + R_2 + \cdots$

  • Parallel: $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$

• Kirchhoff’s Rules:

  • Junction Rule: The sum of currents entering a junction equals the sum leaving.

  • Loop Rule: The sum of potential differences around any closed loop is zero.

• RC Circuits: Circuits containing resistors and capacitors exhibit charging and discharging behavior.

  • Charging: $Q(t) = Q_{max}(1 - e^{-t/RC})$

  • Discharging: $Q(t) = Q_0 e^{-t/RC}$

  • At $t=0$ and $t=\infty$, analyze initial and final conditions.

• Voltmeters and Ammeters: Voltmeters are connected in parallel (high resistance), ammeters in series (low resistance).

Typical Exam Problems

• Apply Kirchhoff’s rules to analyze complex circuits.

• Describe RC circuit behavior during charging and discharging, including at $t=0$ and $t=\infty$.

• Analyze RC circuits with multiple loops.

• Construct an ohmmeter using a voltmeter and ammeter.

Summary Table: Key Quantities in Capacitance and Circuits

Quantity	Symbol	Unit	Key Formula
Capacitance	C	Farad (F)	$C = \frac{Q}{V}$
Charge	Q	Coulomb (C)	$Q = CV$
Voltage	V	Volt (V)	$V = IR$
Current	I	Ampere (A)	$I = \frac{V}{R}$
Resistance	R	Ohm (Ω)	$R = \frac{V}{I}$
Power	P	Watt (W)	$P = IV$

Additional Resources

• Sample problems in the textbook and class notes.

• Homework and tutorial problems (solutions available on D2L).

• Sample exams from other instructors.

• Physics LibreTexts library for further reading.