## PHYS102 Study Guide

### 3a. state Ohm's law in words

1. What happens when a potential difference is applied to the ends of a conductor? What physical quantity measures the rate of the flow of charge?
2. What is the definition of the resistance of a conductor? What is the relationship between resistance, current, and potential difference between the ends of a conductor? When is this relationship called Ohm's Law?

If a conductor is placed in an electric field (for example, if its ends are connected to a battery, so that there is a potential difference between each end), the free charges inside the conductor will begin to move. The rate of the flow of charge is called current: $I=\frac{\mathrm{d}q}{\mathrm{d}t}$. The ratio between the applied potential difference and the current is defined as resistance: $R=\frac{\Delta V}{I}$. For some materials, this ratio is constant, and the conductor is said to obey Ohm's Law. These materials are known as Ohmic materials. In them, the potential difference between the ends of the conductor is proportional to the current through the conductor: $\Delta V=IR$.

Resistance and Ohm's Law are discussed in section 21.6 of Light and Matter and summarized in Ohm's Law.

### 3b. apply Ohm's law to simple circuits

1. Sketch an example of a simple circuit containing a battery and a resistor. What is the relationship between the current in the circuit and the voltage supplied by the battery?

According to Ohm's Law, the current established in a circuit with one battery supplying a voltage $V$ is $I=\frac{V}{R}$. Here, $R$ can be the resistance of the only resistor in the circuit, or the equivalent resistance of the network of several resistance in the circuit.

Watch Circuits and Ohm's Law to review the application of Ohm's Law to a simple circuit.

### 3c. calculate effective resistance of a network of resistors

1. If you have two resistors, how would you connect them to a battery so that they are connected in series? What will the relationship between the current through each resistor be in this case? What will the relationship of the potential differences between the ends of each resistor and the voltage supplied by the battery be? Use these considerations to determine the equivalent resistance of two resistors connected in series.
2. If you have two resistors, how would you connect them to a battery so that they are connected in parallel? What will the relationship between the current through each resistor be in this case? What will the relationship of the potential differences between the ends of each resistor and the voltage supplied by the battery be? Use these considerations to determine the equivalent resistance of two resistors connected in parallel.

When two or more resistors are connected in series:

• They have the same current going through them (this follows from the conservation of charge)
• The sum of the potential differences between the ends of each resistor equals the voltage supplied by the battery
• The equivalent resistance is determined by the formula $R_\mathrm{eq}=R_1+R_2+\cdots$

When two or more capacitors are connected in parallel:

• They have the same potential difference between the ends, which also equals the voltage supplied by the battery
• The sum of currents through each resistor equals the total current in the circuit, or the current drawn from the battery
• The equivalent resistance is determined by the formula $\frac{1}{R_\mathrm{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots$

The series and parallel connection of resistors is discussed in Resistors in Series and in Parallel and can be seen in this solved example of determining an equivalent resistance of a circuit. Also watch Resistors in Series, Resistors in Parallel, and Analyzing a More Complex Resistor Circuit.

### 3d. determine the resistance of a cylindrical wire

1. How do conducting materials resist the flow of a current, at the microscopic level?
2. How does the resistance of a wire depend on the resistivity of the material and the length and cross-sectional area of the wire?

Resistivity is a characteristic of a conducting material and describes its ability to allow charges to flow. It depends on a variety of factors, including the density of atoms in the material and the material's temperature. The resistance of a wire made out of a material with resistivity is proportional to the wire's length (the longer the charges have to travel, the greater the resistance), and inversely proportional to its cross-sectional area (the greater the area, the more pathways for the charges to travel; hence, less resistance), and can be described with $R = \rho\frac{l}{A}$.

An explanation of Ohm's Law on the microscopic level is discussed in Resistance and Resistivity. The formula for the resistance of a wire is applied in this solved example. Also watch Resistivity and Conductivity.

### 3e. compare and contrast voltage and current

1. What conditions are necessary for a current to flow?
2. What are some possible ways to create voltage?

Current is amount of charge passing through the cross-section of a conductor in a unit of time: $I=\frac{\Delta q}{\Delta t}$, or rate of flow of charge: $I=\frac{\mathrm{d}q}{\mathrm{d}t}$. Voltage is the potential difference between two points in space, or between the ends of a conductor. Both quantities are scalar. Current describes the motion of charged particles, whereas voltage measures the energy per unit of charge acquired or lost by these particles.

The ways to establish current and voltage are discussed in sections 21.3 to 21.5 of Light and Matter.

### 3f. use the junction and loop rules to analyze basic circuits

1. What is the junction rule? Explain in terms of conservation of charge.
2. What is the loop rule? Explain in terms of conservative forces and equipotential surfaces.

For some circuits, it is impossible to find an equivalent resistance of a network of resistors. The current through each resistor in such a circuit can still be determined by using Kirchhoff's Rules, which are the Junction Rule and the Loop Rule. These can be applied to any circuit.

The Junction Rule states that the sum of all currents entering a junction equals the sum of all currents leaving a junction.

The Loop Rule states that the algebraic sum of all changes in electric potential due to electromotive forces of the batteries and the voltage drops across the resistors equals zero for any closed loop of a circuit.

Kirchhoff's Rules are explained and illustrated in Kirchhoff's Rules and in this solved example.

### 3g. explain how a battery works

1. Why is a battery a necessary component of an electrical circuit?
2. What is an electromotive force?

A typical battery is an electrochemical cell. The chemical reaction inside the cell separates its positive and negative ions and makes them move in opposite directions. This results in a potential difference between the two ends of an electrical circuit. In this way, the battery converts chemical energy to electrical energy and supplies that energy to the circuit. The amount of energy per unit of charge supplied by the battery is called electromotive force. Despite the name, it is not a force, but rather work per unit charge, which is measured in Volts. For an ideal battery with negligible internal resistance, electromotive force equals the output voltage.

For more about the role of a battery in a circuit, read section 21.5 of Light and Matter, Electric Circuits, and EMF and Internal Resistance.

### 3h. calculate the power in a DC circuit

1. How would you define power using the concepts of work and energy?
2. What are the different ways to calculate the power dissipated by a resistor in DC (direct current) circuits in terms of current, resistance, and voltage?

In electromagnetism, power is defined the same way as in mechanics: it is a rate at which work is performed, or rate at which energy is dissipated: $P=\frac{\mathrm{d}W}{\mathrm{d}t}$, or $P=\frac{\mathrm{d}E}{\mathrm{d}t}$. As charges move through a conductor, they lose energy, which gets converted into thermal energy or light. The power dissipated by resistor $R$ with current $I$ going through it can be calculated as $P=I^2 R$. Alternatively, since the voltage across the resistor is $\Delta V = IR$, the power can be calculated as $P=I\Delta V=\frac{\left ( \Delta V \right )^2}{R}$.

To review, read Energy in DC Circuits and this solved example.

### Unit 3 Vocabulary

This vocabulary list includes terms that might help you with the review items above and some terms you should be familiar with to be successful in completing the final exam for the course.

Try to think of the reason why each term is included.

• Battery
• Conductivity
• Current
• Electromotive Force (EMF)
• Kirchhoff's Rules: Junction Rule and Loop Rule
• Ohm's Law
• Parallel connection
• Power
• Resistance
• Resistivity
• Resistor
• Series connection
• Voltage