3.2 Ohm’s law: resistance and simple circuits

Resistances range over many orders of magnitude. Some ceramic insulators, such as those used to support power lines, have resistances of ${\text{10}}^{\text{12}}\Omega$ or more. A dry person may have a hand-to-foot resistance of ${\text{10}}^5\Omega$ , whereas the resistance of the human heart is about ${\text{10}}^3\Omega$ . A meter-long piece of large-diameter copper wire may have a resistance of ${\text{10}}^{-5}\Omega$ , and superconductors have no resistance at all (they are non-ohmic). Resistance is related to the shape of an object and the material of which it is composed, as will be seen in Resistance and Resistivity .

Additional insight is gained by solving $I=\text{V/R}$ for $V,$ yielding

This expression for $V$ can be interpreted as the voltage drop across a resistor produced by the flow of current $I$ . The phrase $\text{IR}$ drop is often used for this voltage. For instance, the headlight in [link] has an $\text{IR}$ drop of 12.0 V. If voltage is measured at various points in a circuit, it will be seen to increase at the voltage source and decrease at the resistor. Voltage is similar to fluid pressure. The voltage source is like a pump, creating a pressure difference, causing current—the flow of charge. The resistor is like a pipe that reduces pressure and limits flow because of its resistance. Conservation of energy has important consequences here. The voltage source supplies energy (causing an electric field and a current), and the resistor converts it to another form (such as thermal energy). In a simple circuit (one with a single simple resistor), the voltage supplied by the source equals the voltage drop across the resistor, since $\text{PE}=q\mathrm{\Delta }V$ , and the same $q$ flows through each. Thus the energy supplied by the voltage source and the energy converted by the resistor are equal. (See [link] .)

Phet explorations: ohm's law

See how the equation form of Ohm's law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm's law. The sizes of the symbols in the equation change to match the circuit diagram.

Section summary

• A simple circuit is one in which there is a single voltage source and a single resistance.
• One statement of Ohm’s law gives the relationship between current $I$ , voltage $V$ , and resistance $R$ in a simple circuit to be $I=\frac{V}{R}.$
• Resistance has units of ohms ( $\text{Ω}$ ), related to volts and amperes by $\mathrm{1\; \Omega }=\text{1 V/A}$ .
• There is a voltage or $\text{IR}$ drop across a resistor, caused by the current flowing through it, given by $V=\text{IR}$ .

Conceptual questions

Problems&Exercises