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:. The ratio between the applied potential difference and the current is defined as resistance: . 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: .
According to Ohm's Law, the current established in a circuit with one battery supplying a voltageis . Here, 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.
When two or more resistors are connected in series:
When two or more capacitors are connected in parallel:
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.
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.
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.
Current is amount of charge passing through the cross-section of a conductor in a unit of time:, or rate of flow of charge: . 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.
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.
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.
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:, or . As charges move through a conductor, they lose energy, which gets converted into thermal energy or light. The power dissipated by resistor with current going through it can be calculated as . Alternatively, since the voltage across the resistor is , the power can be calculated as .
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.