- Electric current is the rate at which charge flows, given by where is the amount of charge passing through an area in time .
- The direction of conventional current is taken as the direction in which positive charge moves.
- The SI unit for current is the ampere (A), where
- Current is the flow of free charges, such as electrons and ions.
- Drift velocity is the average speed at which these charges move.
- Current is proportional to drift velocity , as expressed in the relationship . Here, is the current through a wire of cross-sectional area . The wire’s material has a free-charge density , and each carrier has charge and a drift velocity .
- Electrical signals travel at speeds about times greater than the drift velocity of free electrons.
20.2 Ohm’s Law: Resistance and Simple Circuits
- 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 , voltage , and resistance in a simple circuit to be
- Resistance has units of ohms (), related to volts and amperes by .
- There is a voltage or drop across a resistor, caused by the current flowing through it, given by .
20.3 Resistance and Resistivity
- The resistance of a cylinder of length and cross-sectional area is , where is the resistivity of the material.
- Values of in Table 20.1 show that materials fall into three groups—conductors, semiconductors, and insulators.
- Temperature affects resistivity; for relatively small temperature changes , resistivity is , where is the original resistivity and is the temperature coefficient of resistivity.
- Table 20.2 gives values for , the temperature coefficient of resistivity.
- The resistance of an object also varies with temperature: , where is the original resistance, and is the resistance after the temperature change.
20.4 Electric Power and Energy
- Electric power is the rate (in watts) that energy is supplied by a source or dissipated by a device.
- Three expressions for electrical power are
- The energy used by a device with a power over a time is .
20.5 Alternating Current versus Direct Current
- Direct current (DC) is the flow of electric current in only one direction. It refers to systems where the source voltage is constant.
- The voltage source of an alternating current (AC) system puts out , where is the voltage at time , is the peak voltage, and is the frequency in hertz.
- In a simple circuit, and AC current is , where is the current at time , and is the peak current.
- The average AC power is .
- Average (rms) current and average (rms) voltage are and , where rms stands for root mean square.
- Thus, .
- Ohm’s law for AC is .
- Expressions for the average power of an AC circuit are , , and , analogous to the expressions for DC circuits.
20.6 Electric Hazards and the Human Body
- The two types of electric hazards are thermal (excessive power) and shock (current through a person).
- Shock severity is determined by current, path, duration, and AC frequency.
- Table 20.3 lists shock hazards as a function of current.
- Figure 20.25 graphs the threshold current for two hazards as a function of frequency.
20.7 Nerve Conduction–Electrocardiograms
- Electric potentials in neurons and other cells are created by ionic concentration differences across semipermeable membranes.
- Stimuli change the permeability and create action potentials that propagate along neurons.
- Myelin sheaths speed this process and reduce the needed energy input.
- This process in the heart can be measured with an electrocardiogram (ECG).