5.2b Resistance

THE IB SAYS

Essential idea: One of the earliest uses for electricity was to produce light and heat. This technology continues to have a major impact on the lives of people around the world.

Understandings: Resistance expressed as R=V/I; Ohm's law

Applications and skills: Identifying ohmic / non-ohmic conductors with V/I graphs; Solving problems involving pd, current, charge, power, resistance and resistivity; Experimentally investigating factors that affect resistance

Guidance: The filament lamp should be described as a non-ohmic device; a metal wire at a constant temperature is an ohmic device.

Data booklet equations: R=V/I; P=VI=I²R=V²/R

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The divisions of an electrical circuit

All electrical circuits are made from a variety, and often a great number, of different components. I find it useful to divide these parts into three categories: sources, load and wire.

Sources - These contribute EMF. Without a source there can be no current.
Load - The load is the collective term for the components that convert the electrical energy to heat (sometimes via another energy type)
Wire - Also known as cable, connectors, rails, etc. These component carry the electrical energy between sources and loads, idelly without energy loss.

Resistance

An electrical field, resulting from charges, will result in a current, a flow of charge. How much current (in Amps) results from the applied EMF (from the source) depends on a property of the circuit called resistance.

Resistance can be described as "the degree to which a substance or device opposes the passage of an electric current" (Oxford English Dictionary) but a more precise definition would be the potential difference [in volts] required to create a current of 1 amp. Thus R (resistance) = V / I. The unit of resistance is the Ohm [Ω]. A resistance of 1Ω means a current of 1A will flow when a potential difference of 1V is applied.

The ohm is named for Gregor Ohm who proposed Ohm's Law - that in a conductor, the current induced is directly proportional to the proportional difference - i.e. doubling the potential difference, doubles the current. This law is, however, only valid for some conductors, and even then only in some conditions to a limited degree. One major factor that Ohm's Law fails to account for is different temperatures.

Voltage-Current (V I) Graphs

For an ohmic conductor (one that obey's Ohm's Law) a graph of potential difference against current will be a straight line. The closest examples to Ohmic conductors in real life and resistors, used in circuits to control the flow and supply of electrical current and potential difference. In particular this includes fixed resistors, whose resistance is constant(ish) over a range of potential differences and temperatures, and variable resistors, whose resistance is similarly constant unless adjusted by the user.

A V-I graph for a fixed resistor, a conductor that obeys Ohm's Law.

A V-I graph for a filament lightbulb, a non-ohmic conductor.

A V-I graph for a diode, a non-ohmic conductor that only permits electricity to flow in one direction, and whose resistance decreases with potential difference in that direction. This is a characteristic of some semiconductor based materials.

A V-I graph for a thermistor. As it carries current its temperature rises and resistance decreases.

Power and resistance

By combining the equation for power, P = VI, and the definition of resistance, V = IR, we may derive two further forms of the power equation. These are P = I²R and P = V²/R. Both of these equations may save you time by removing the need to calculate current or potential difference if it is not provided.

Resources from textbooks

Oxford Physics: pages 196 - 201

Hamper HL (2014): pages 220 - 222

Relevant questions from Dot Point Physics (5 Electric currents)

pages 233 - 235

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