Current and Circuits Notes

Current and Circuits

Focus Question

• What is an electric circuit?

New Vocabulary

• Electric current: The flow of charged particles.

• Conventional current: The direction in which a positive test charge moves.

• Battery: A device made up of several galvanic cells connected together, converting chemical energy to electrical energy.

• Electric circuit: Any closed loop or conducting path allowing electric charges to flow.

• Ampere (A): The SI unit for electric current, equal to a flow of one coulomb per second.

• Resistance: The property determining how much current will flow.

• Resistor: A device designed to have a specific resistance.

• Parallel connection: A connection where the current has two or more paths to follow.

• Series connection: A connection with only one current path.

Review Vocabulary

• Electric potential difference: The work needed to move a positive test charge from one point to another, divided by the magnitude of the test charge.

Producing Electric Current

• When two conductors touch, charges flow from the sphere at a higher potential to the one at a lower potential until there is no potential difference between them.

• A flow of charged particles is an electric current.

• The direction in which a positive test charge moves is called conventional current.

• Usually, it is the negative charges (electrons) that flow.

• The flow of electrons and the direction of the conventional current are in opposite directions.

• Electric potential difference between two points can be maintained by pumping charged particles from the lower potential back to the higher potential.

• The pump increases the electric potential energy of the charges and requires an external energy source to run.

• Energy sources include:

  • Voltaic or galvanic cell (dry cell): Converts chemical energy to electric energy.

  • Battery: Several galvanic cells connected together.

  • Photovoltaic cell or solar cell: Changes light energy into electric energy.

Electric Circuits

• Any closed loop or conducting path allowing electric charges to flow is called an electric circuit.

• A circuit includes:

  • A charge pump: Increases the potential energy of the charges flowing from A to B.

  • A device: Reduces the potential energy of the charges flowing from B to A.

• The potential energy lost by the charges ($q\Delta V$) moving through the device is usually converted into some other form of energy.

• Charge is a conserved quantity; it cannot be created or destroyed, but it can be separated.

• The total amount of charge in the circuit (number of negative electrons and positive ions) does not change.

• Energy is also conserved.

• The change in electric energy ($\Delta E$) equals $q\Delta V$.

• The net change in potential energy of the charges going completely around the circuit must be zero because charge is conserved.

Rates of Charge Flow and Energy Transfer

• The rate of flow of electric charge ($q/t$) is called electric current and is represented by $I$, so $I = q/t$.

• The SI unit for electric current is the ampere (A), which is equal to a flow of one coulomb per second.

• The energy carried by an electric current depends on the charge transferred ($q$) and the potential difference across which it moves ($\Delta V$). Thus, $E = q\Delta V$.

• To find the power delivered to an electrical device, use $P = E/t$ and substitute $E = q\Delta V$ and $q = I t$. Therefore, Power $P = I\Delta V$

Example Problem

• A 120-V motor operates at 13 A. Determine the power and the energy used in one hour of operation.

• Known:

  • $\Delta V = 120 V$

  • $I = 13 A$

  • $t = 1 h = 3600 s$

• Unknown:

  • $P = ?$

  • $E = ?$

• Solution:

  • Use the relationship among power, current, and voltage: $P = I\Delta V = (13 A)(120 V) = 1560 W$

  • Use the relationship among energy, power, and time: $E = Pt = (1560 W)(3600 s) = 5.6 \times 10^6 J$

Diagramming Circuits

• A circuit can be described in:

  • Words

  • A photograph or an artist’s drawing

  • Schematics called circuit diagrams

Common Circuit Symbols

• Conductor

• Switch

• Resistor (fixed)

• Ground

• Battery

• Potentiometer (variable resistor)

• Lamp

• DC generator

• Fuse

• Capacitor

• Inductor

• Voltmeter

• Ammeter

Resistance and Ohm’s Law

• The property determining how much current will flow is called resistance.

• Resistance is measured by placing a potential difference across a conductor and dividing the voltage by the current.

• The resistance ($R$) is defined as the ratio of electric potential difference ($\Delta V$) to the current ($I$): $R = \frac{\Delta V}{I}$

• The resistance of a conductor is measured in ohms ($\Omega$).

• One ohm ($1 \Omega$) is the resistance permitting an electric charge of 1 A to flow when a potential difference of 1 V is applied across the resistance.

• There are two ways to control the current in a circuit: Vary $V$, $R$, or both, because $I = \frac{\Delta V}{R}$.

• A device having constant resistance independent of the potential difference is said to obey Ohm’s law.

• Most metallic conductors obey Ohm’s law, at least over a limited range of voltages.

• Transistors and diodes are important electronic components that do not obey Ohm’s law.

• A resistor is a device designed to have a specific resistance.

• Resistors may be made of graphite, semiconductors, or wires that are long and thin.

• A variable resistor, called a potentiometer, can be used to control the current in circuits or parts of circuits.

Example Problem

• A 9.0-V battery is connected to a 15-k$\Omega$ resistor. What is the current in this circuit?

• Known:

  • $\Delta V = 9.0 V$

  • $R = 15 k\Omega = 15 \times 10^3 \Omega$

• Unknown:

  • $I = ?$

• Solution:

  • Use the relationship among current, potential difference, and resistance: $I = \frac{V}{R} = \frac{9.0 V}{15 \times 10^3 \Omega} = 0.60 \times 10^{-3} A = 0.60 mA$

Parallel and Series Connections

• When a voltmeter is connected across another component, it is called a parallel connection because the circuit component and the voltmeter are aligned parallel to each other in the circuit.

• Anytime the current has two or more paths to follow, the connection is a parallel connection.

• The potential difference across the voltmeter is equal to the potential difference across the circuit element.

• Always associate the words voltage across with a parallel connection.

• An ammeter measures the current through a circuit component.

• The same current going through the component must go through the ammeter, so there can be only one current path.

• A connection with only one current path is called a series connection.

• Always associate the words current through with a series connection.

Quiz Answers

• 1. How is conventional current defined? C: The direction that a positive test charge moves.

• 2. In the transformation of potential energy to electrical energy, which factor does NOT contribute to thermal energy production? A: flashes of light

• 3. What is conserved in an electric circuit? D: charge

• 4. Which is the correct formula for resistance? R = $\frac{\Delta V}{I}$

• 5. If current has two or more paths to follow, what kind of connection is it? B: parallel