Electric Current Resistance and Ohm's Law Lesson 26 by Owen Borville 12.27.2025
Electric Current I is the average rate at which charge flows: Iave = ΔQ/Δt where ΔQ is the amount of charge passing through an area in time Δt. The instantaneous electric current I is the rate at which charge flows. The limit as the change in time approaches zero is I = dQ/dt, where dQ/dt is the time derivative of the charge.
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 1 A = 1 C/s. (C = Coulomb, s = second). Current is the flow of free charges, such as electrons, protons, and ions. Drift velocity (vd) is the average speed at which these charges move (vd = I/nqA, where n is the number density of charge carriers, q is the charge of a single carrier, and A is the cross sectional area of the conductor).
The current through a conductor (metal) depends mainly on the motion of free electrons. When an electric field is applied to a conductor, the free electrons in a conductor do not move through a conductor at a constant speed and direction, however, but rather move in near random motion due to collisions with atoms and other free electrons. When an electrical field is applied to the conductor, however, the overall velocity of the electrons can be defined in terms of a drift velocity.
The current density is a vector quantity defined as the current through an infinitesimal area divided by the area. The current can be calculated from the current density by I = ∫∫(area) J*dA.
An incandescent light bulb is a filament of wire enclosed in a glass bulb that is partially evacuated. Current runs through the filament, where the electrical energy is converted to light and heat.
Current I is proportional to drift velocity vd (I = nqAvd) I is the current through a wire of cross-sectional area A. The wire's material has a free-charge density n, and each carrier has a charge q and a drift velocity vd. Electrical signals travel at speeds about 10^12 times greater than the drift velocity of free electrons.
A simple circuit is one in which there is a single voltage source and a single resistance. Ohm's law gives the relationship between current I, voltage V, and resistance R in a simple circuit: V = I*R or I = V/R or R = V/I. Ohm's law applies to simple circuits and resistors, but not to some other devices.
Resistance has units of ohms (Ω), which is related to volts and amperes by 1 Ω = 1 V/A. There is a voltage or IR drop across a resistor, caused by the current flowing through it, given by V = IR. At the microscopic level, Ohm's law is J = σE.
The resistance R of a cylinder of length L and cross-sectional area A is R = ρL/A, where ρ is the resistivity of the material. Reference table values of ρ show that materials fall into three groups: conductors, semiconductors, and insulators.
The resistivity equation ρ = E/J defines material resistivity ρ as the ratio of the electric field E to the current density J within it so that ρ quantifies how strongly a material substance resists or opposes electric current flow, independent of shape, unlike electrical resistance R which depends on the material of an object and its dimensions of length and area.
Temperatures affect resistivity. For relatively small temperature changes ΔT, resistivity is ρ = ρ0(1+αΔT), where ρ0 is the original resistivity and α is the temperature coefficient of resistivity. Values for α are found in reference tables, the temperature coefficient of resistivity. The resistance R of an object also varies with temperature R = R0(1+αΔT), where R0 is the original resistance, and R is the resistance after the temperature change.
Electric power P is the rate (in watts) that energy is supplied by a source circuit or dissipated or consumed by a device. Electrical power P is calculated by three equations:
P = I*V or P = V^2/R or P = I^2*R The energy used by a device with a power P over a time t is E = P*t. The SI unit for electric power is the watt and the SI unit for electric energy is the joule. Another common unit for electric energy (used by electric power companies) is the kilowatt-hour (kW*h). The total energy used over a time interval can be calculated by integration: E = ∫Pdt.
Direct current (DC) is the flow of electric current in only one direction and it refers to systems where the source voltage is constant. The voltage source of an alternating current (AC) system puts out V = V0sin2π𝑓t, where V is the voltage at time t, Vo is the peak voltage, and 𝑓 is the frequency in hertz.
In a simple circuit, I = V/R and AC current is I = I0sin 2π𝑓t, where I is the current at time t, and I0 = V0/R is the peak current.
The average AC power is Pave = 1/2I0V0.
Average (rms) current Irms and average (rms) voltage Vrms are Irms = I0/√2 and Vrms = V0/√2, where rms stands for root mean square.
Therefore, Pave = Irms*Vrms
Ohm's law for AC is Irms = Vrms/R
Expressions for the average power of an AC circuit are Pave = IrmsVrms, Pave = Vrms^2/R and Pave = Irms^2R analogous to the expressions for DC circuits.
Electric hazards to the human body include thermal (excessive power) and shock (current through a person). Shock severity is determined by current, path, duration, and AC frequency. Shock hazards as a function of current are listed in reference tables. The threshold current for two hazards as a function of frequency can be shown on a graph.
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).
Superconductivity is a phenomenon that occurs in some materials when cooled to very low critical temperatures, resulting in a resistance of exactly zero and the expulsion of all magnetic fields. Materials that are normally good conductors (such as copper, gold, and silver) do not experience superconductivity. Superconductivity was first observed in mercury by Heike Kamerlingh Onnes in 1911. In 1986, Dr. Ching Wu Chu of Houston University fabricated a brittle, ceramic compound with a critical temperature close to the temperature of liquid nitrogen. Superconductivity can be used in the manufacture of superconducting magnets for use in MRI machines and high-speed levitated (maglev) trains. Particle accelerators have also used superconductors, in addition to advanced medical diagnosis, fundamental physics research, power transmission, electric motors and generators, energy storage, quantum computing, and sensitive magnetic field detectors.
Electric Current I is the average rate at which charge flows: Iave = ΔQ/Δt where ΔQ is the amount of charge passing through an area in time Δt. The instantaneous electric current I is the rate at which charge flows. The limit as the change in time approaches zero is I = dQ/dt, where dQ/dt is the time derivative of the charge.
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 1 A = 1 C/s. (C = Coulomb, s = second). Current is the flow of free charges, such as electrons, protons, and ions. Drift velocity (vd) is the average speed at which these charges move (vd = I/nqA, where n is the number density of charge carriers, q is the charge of a single carrier, and A is the cross sectional area of the conductor).
The current through a conductor (metal) depends mainly on the motion of free electrons. When an electric field is applied to a conductor, the free electrons in a conductor do not move through a conductor at a constant speed and direction, however, but rather move in near random motion due to collisions with atoms and other free electrons. When an electrical field is applied to the conductor, however, the overall velocity of the electrons can be defined in terms of a drift velocity.
The current density is a vector quantity defined as the current through an infinitesimal area divided by the area. The current can be calculated from the current density by I = ∫∫(area) J*dA.
An incandescent light bulb is a filament of wire enclosed in a glass bulb that is partially evacuated. Current runs through the filament, where the electrical energy is converted to light and heat.
Current I is proportional to drift velocity vd (I = nqAvd) I is the current through a wire of cross-sectional area A. The wire's material has a free-charge density n, and each carrier has a charge q and a drift velocity vd. Electrical signals travel at speeds about 10^12 times greater than the drift velocity of free electrons.
A simple circuit is one in which there is a single voltage source and a single resistance. Ohm's law gives the relationship between current I, voltage V, and resistance R in a simple circuit: V = I*R or I = V/R or R = V/I. Ohm's law applies to simple circuits and resistors, but not to some other devices.
Resistance has units of ohms (Ω), which is related to volts and amperes by 1 Ω = 1 V/A. There is a voltage or IR drop across a resistor, caused by the current flowing through it, given by V = IR. At the microscopic level, Ohm's law is J = σE.
The resistance R of a cylinder of length L and cross-sectional area A is R = ρL/A, where ρ is the resistivity of the material. Reference table values of ρ show that materials fall into three groups: conductors, semiconductors, and insulators.
The resistivity equation ρ = E/J defines material resistivity ρ as the ratio of the electric field E to the current density J within it so that ρ quantifies how strongly a material substance resists or opposes electric current flow, independent of shape, unlike electrical resistance R which depends on the material of an object and its dimensions of length and area.
Temperatures affect resistivity. For relatively small temperature changes ΔT, resistivity is ρ = ρ0(1+αΔT), where ρ0 is the original resistivity and α is the temperature coefficient of resistivity. Values for α are found in reference tables, the temperature coefficient of resistivity. The resistance R of an object also varies with temperature R = R0(1+αΔT), where R0 is the original resistance, and R is the resistance after the temperature change.
Electric power P is the rate (in watts) that energy is supplied by a source circuit or dissipated or consumed by a device. Electrical power P is calculated by three equations:
P = I*V or P = V^2/R or P = I^2*R The energy used by a device with a power P over a time t is E = P*t. The SI unit for electric power is the watt and the SI unit for electric energy is the joule. Another common unit for electric energy (used by electric power companies) is the kilowatt-hour (kW*h). The total energy used over a time interval can be calculated by integration: E = ∫Pdt.
Direct current (DC) is the flow of electric current in only one direction and it refers to systems where the source voltage is constant. The voltage source of an alternating current (AC) system puts out V = V0sin2π𝑓t, where V is the voltage at time t, Vo is the peak voltage, and 𝑓 is the frequency in hertz.
In a simple circuit, I = V/R and AC current is I = I0sin 2π𝑓t, where I is the current at time t, and I0 = V0/R is the peak current.
The average AC power is Pave = 1/2I0V0.
Average (rms) current Irms and average (rms) voltage Vrms are Irms = I0/√2 and Vrms = V0/√2, where rms stands for root mean square.
Therefore, Pave = Irms*Vrms
Ohm's law for AC is Irms = Vrms/R
Expressions for the average power of an AC circuit are Pave = IrmsVrms, Pave = Vrms^2/R and Pave = Irms^2R analogous to the expressions for DC circuits.
Electric hazards to the human body include thermal (excessive power) and shock (current through a person). Shock severity is determined by current, path, duration, and AC frequency. Shock hazards as a function of current are listed in reference tables. The threshold current for two hazards as a function of frequency can be shown on a graph.
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).
Superconductivity is a phenomenon that occurs in some materials when cooled to very low critical temperatures, resulting in a resistance of exactly zero and the expulsion of all magnetic fields. Materials that are normally good conductors (such as copper, gold, and silver) do not experience superconductivity. Superconductivity was first observed in mercury by Heike Kamerlingh Onnes in 1911. In 1986, Dr. Ching Wu Chu of Houston University fabricated a brittle, ceramic compound with a critical temperature close to the temperature of liquid nitrogen. Superconductivity can be used in the manufacture of superconducting magnets for use in MRI machines and high-speed levitated (maglev) trains. Particle accelerators have also used superconductors, in addition to advanced medical diagnosis, fundamental physics research, power transmission, electric motors and generators, energy storage, quantum computing, and sensitive magnetic field detectors.