7.10 Ohm’s law: resistance and simple circuits  (Page 2/7)

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.

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] .)

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