Chapter 18
Electric Currents
Higher maximum
current from batteries
Higher voltage
Chapter 18
• Electric Current
• Ohm’s Law: Resistance and Resistors
• Resistivity of a material
• Electric Power
• Power in Household Circuits
• Alternating Current
• Microscopic View of Electric Current
Electric Current
Electric current is the rate of flow of charge through a conductor:
This is more specifically the charge that moves past any point per unit time.
Unit of electric current: the ampere, A.
1 A = 1 C/s
Electric Current
By convention, current is defined as flowing from + to ­ . Electrons actually flow in the opposite direction, but not all currents consist of electrons.
Resistance and Resistors
The ratio of voltage to current is called the resistance:
Ohm’s Law:
Unit of resistance: the ohm, Ω.
1 Ω = 1 V/A
Ohm’s Law: Resistance and Resistors
In many conductors, the resistance is independent of the voltage; this relationship is called Ohm’s law. Materials that do not follow Ohm’s law are called nonohmic: b) is for a diode
Ohm’s Law: Resistance and Resistors
Some clarifications:
• Batteries maintain a (nearly) constant potential difference; current varies depending on the ‘load’.
• Resistance is a property of a material or device.
• Current is not a vector but it does have a direction ­ from positive toward negative potential
• Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.
Resistivity
The resistance of a wire is directly proportional to its length and inversely proportional to its cross­sectional area:
The constant ρ, called the resistivity, is characteristic of the material. This equation is specific to a geometry having a constant cross sectional area (like a cylinder) with current flowing along the length
Resistivity of Specific Materials
Resistivity: Temperature Dependence
For metals, resistivity increases with temperature:
This is also true for most insulators; however, Semiconductors are complex materials, and often have resistivities that decrease with T .
Electric Power
Power, as in kinematics, is the energy transformed by a device per unit time:
Electric Power (DC)
The unit of power is the watt, W.
For ohmic devices, we can make the substitutions:
Alternating Current
Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC).
Alternating Current
The voltage varies sinusoidally with time:
as does the current:
(18­7)
Alternating Current
Multiplying current and voltage gives the power:
Average power
Alternating Current
Usually we are interested in the average power:
Alternating Current
The current and voltage both have average values of zero, so we square them, take the average, then take the square root.
This is called the root mean square (rms) value.
For AC Pave = I
rms Vrms
Microscopic View of Electric Current
Electrons in a conductor have large, random speeds just due to temperature. When a potential difference is applied, the electrons also acquire an average drift velocity, which is generally considerably smaller than the thermal velocity.
Microscopic View of Electric Current
This drift speed is related to the current in the wire, and also to the number of electrons per unit volume.
So
Or “current density” I /A = nevd
Summary of Chapter 18
• Electric current is the rate of flow of electric charge.
• Conventional current is in the direction that positive charge would flow.
• Resistance is the ratio of voltage to current:
• Ohmic materials have constant resistance, independent of voltage.
Summary of Chapter 18
• Resistance is determined by shape and material:
• ρ is the resistivity, and is a material property.
• Power in an electric circuit: • Direct current is constant
• Relation between drift speed and current:
Summary of Chapter 18
• Alternating current varies sinusoidally • The average (rms) current and voltage: