A micro-course in electric current covering the concepts of Ohm’s law, electric potential and power consumption in a resistor, and electromotive force, for high school students.
What is an Electric Current?
When there is a electric potential difference between two points, and there is a electric conductor between these two points, electric charge can move from higher electric potential to the lower one (similar to the flow of water from a higher point to the lower one in a gravitational field). flow of the electric charge is called electric current. Electric charge can be carried by electrons, ions, or both of them.
By moving electrons in a wire, electric current can be created. In a wire electrons move from lower electric potential to a higher electric potential. So the direction of electric current in a wire is opposite to the direction of the motion of electrons in the wire.
Inside electrolytes, ions (negative and positive) carry electric charges; and in a plasma charge carriers are both electrons and ions.
Electric current causes heating; it also creates magnetic field, and it can also create light.
The value of electric current 'I', is the amount of electric charge transferred through a surface, per unit time. In a charge carrying wire, this surface is the cross section of the wire. So the average value of electric current is given by this equation:
The SI unit of electric current is Ampere (A); one Ampere is one Coulomb per second.
So the instantaneous value of electric current can be found as:
If the average value of electric current is constant over different intervals of time (so the instantaneous and average values of electric current are the same), the electric current is called direct electric current.
Ohm’s Law
Electric current passing through a resistor R, is directly proportional to the
electric potential difference between its end points.
electric potential difference between its end points.
According to the Ohm’s law electric current 'I', between two points of a conductor is directly proportional to the electric potential difference (voltage), ∆V or simply 'V' , between them:
where 1/R is the coefficient of proportionality; and 'R' itself is the amount of electric resistance between two points.
SI unit of resistance is ohm (Ω ). One ohm is the resistance between two points, if electric potential difference between them is one volt and electric current of one ampere is flowing between them.
Electric Resistance of Materials
If a given material has uniform cross section, its resistance can be computed as:
where 'L' is the length of material, and 'A' is the area of its cross section. 'ρ' is the electrical resistivity (or specific electrical resistance) of the material, measured in ohm-metres (Ω.m). The resistivity is proportionality constant, and it depends only on the material.
Resistance changes with temperature too. 'R' is a nonlinear equation of temperature 'T' , but for very small variation of temperature, R(T ) can be approximated by a linear equation:
where 'T0' is a fixed reference temperature (usually room temperature) measured in Kelvins (K); and 'R0' is the resistance at temperature 'T0'.
'α' is called the temperature coefficient of resistance, and it has different values for different reference temperatures.
Electric Potential and Power Consumption in a Resistor
Electric potential decline (or voltage drop) across a resistor 'R', between two points, A and B, in a electric circuit carrying electric current of 'I', can be found as:
This equation is in fact Ohm’s law; and in this equation, 'VA' and 'VB' are electric potential at points A and B. So while electric charge is moving from a higher potential (point A) to the lower one (point B), its potential energy decreases as:
This energy can be released as heat, light,...
When electric current is constant, i.e., q = It, the equation above can be written as:
So this is the electric energy consumed by a resistor 'R', in a time interval of 't', if a constant electric current 'I' is passing through it. The power consumption of this resistor can also be found as:
You can write this equation as:
Power is measured in watt (W ), that is joules per second. Energy consumption is also measured in watt-hour (W −h), or kilo watt-hour (kW −h), in addition to the joules (J). One watt-hour is energy consumption in time interval of one hour, if the power consumption is one watt.
Electromotive Force
Electromotive force (or emf), represented by ε and measured in volt, is the electric potential difference (or voltage) created by a electrical energy source that transforms other forms of energy to the electrical energy. The generated voltage is the work done per unit charge that is stored as electric potential energy per unit charge.
So emf is not a force, although it is called "force" traditionally.
In this circuit emf source is a battery. So it creates a direct current, I, in the circuit.
Batteries and electric generators are examples of emf sources. Batteries convert chemical energy to electric potential energy, and electric generators convert mechanical energy to electricity.
Source of a electrical energy has an internal resistance, and in a electric circuit, this resistance must be considered as one of the components of the circuit.
In the picture above, a direct current 'I', is created by a battery. Internal electric resistance of battery is represented by 'r', and 'ε' is the voltage of battery. So we have:
and,
where 'Ir' is electric potential drop inside the battery (emf source).
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