Electric Current and Circuits Notes

Electric Current

• Electric current is the flow of electric charges.

Key Questions

• What is electric current?
• How does energy change in electric circuits?
• What is Ohm’s law?
• How are power, current, potential difference, and resistance mathematically related?

Vocabulary

• Electric current
• Conventional current
• Battery
• Electric circuit
• Ampere
• Resistance
• Resistor
• Parallel connection
• Series connection

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 the two conductors.
• A flow of charged particles is an electric current.
• The direction in which a positive test charge moves is called conventional current.
• Usually, negative charges (electrons) 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 it requires an external energy source to run.
• A voltaic or galvanic cell (a common dry cell) converts chemical energy to electric energy. A battery is made up of several galvanic cells connected together.
• A 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, which increases the potential energy of the charges flowing from A to B, and a device that 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. Charges cannot be created or destroyed, but they can be separated.
• The total amount of charge in the circuit does not change.
• Energy is also conserved.
• The change in electric energy $(\Delta E)$ equals $q \Delta V$.
• Because charge is conserved, the net change in potential energy of the charges going completely around the circuit must be zero.

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 $q = I t$.

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:
    • $P = ?$
    • $E = ?$
  • Solve for the unknown:
    • Use the relationship among power, current, and voltage: $P = I \Delta V = (13 A)(120 V) = 1600 W$
    • Use the relationship among energy, power, and time: $E = Pt = (1600 W)(3600 s) = 5.8 \times 10^6 J$

Diagramming Circuits

• A circuit can be described:
  • In words
  • In a photograph or an artist’s drawing
  • In schematics called circuit diagrams

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.
• Because $I = \frac{\Delta V}{R}$, $I$ can be changed by varying $V$, $R$, or both.
• 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 2

• Problem: A 9.0-V battery is connected to a 15-k$\Omega$ resistor. What is the current in this circuit?
  • Known:
    • $\Delta V = 9.0 V$
    • $R = 15 k\Omega$
  • Unknown: $I = ?$
  • Solution: $I = \frac{V}{R} = \frac{9.0 V}{15 \times 10^3 \Omega} = 0.60 \times 10^{-3} A = 0.60 mA$

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.