The relationship between Voltage, Current and
Resistance in any DC electrical circuit was firstly discovered by the German physicist
Georg Ohm, (1787 - 1854). Georg Ohm found that, at a constant temperature, the
electrical current flowing through a fixed linear resistance is directly proportional to the voltage applied across
it, and also inversely proportional to the resistance. This relationship between the Voltage,
Current and Resistance forms the bases of Ohms Law
and is shown below.
Ohms Law Relationship
By knowing any two values of the Voltage,
Current or Resistance quantities we can use Ohms Law
to find the third missing value. Ohms Law is used extensively in electronics formulas and calculations
so it is "very important to understand and accurately remember these formulas".
To find the Voltage, ( V )
[ V = I x R ] V (volts)
= I (amps) x R (Ω)
To find the Current, ( I )
[ I = V ÷ R ] I (amps)
= V (volts) ÷ R (Ω)
To find the Resistance, ( R )
[ R = V ÷ I ] R
(Ω) = V (volts) ÷ I (amps)
It is sometimes easier to remember Ohms law relationship by using pictures. Here the three quantities
of V, I and R have been superimposed into
a triangle (affectionately called the Ohms Law Triangle) giving voltage at the top with current and
resistance at the bottom. This arrangement represents the actual position of each quantity in the Ohms law formulas.
Ohms Law Triangle
and transposing the above Ohms Law equation gives us the following combinations of the same equation:
Then by using Ohms Law we can see that a voltage of 1V applied to a resistor of 1Ω will
cause a current of 1A to flow and the greater the resistance, the less current will flow for any applied voltage.
Any Electrical device or component that obeys "Ohms Law" that is, the current flowing through it is proportional
to the voltage across it ( I α V ), such as resistors or cables, are said to be
"Ohmic" in nature, and devices that do not, such as transistors or diodes, are said to be "Non-ohmic"
Power in Electrical Circuits
Electrical Power, ( P ) in a circuit is the amount of energy that is
absorbed or produced within the circuit. A source of energy such as a voltage will produce or deliver power while the
connected load absorbs it. The quantity symbol for power is P and is the product of voltage
multiplied by the current with the unit of measurement being the Watt ( W ) with prefixes used to denote
milliwatts (mW = 10-3W) or kilowatts
(kW = 103W). By using Ohm's law and substituting for V,
I and R the formula for electrical power can be found as:
To find the Power (P)
[ P = V x I ] P (watts)
= V (volts) x I (amps)
[ P = V2 ÷ R ] P
(watts) = V2 (volts) ÷ R (Ω)
[ P = I2 x R ] P
(watts) = I2 (amps) x R (Ω)
Again, the three quantities have been superimposed into a triangle this time called the
Power Triangle with power at the top and current and voltage at the bottom. Again, this arrangement
represents the actual position of each quantity in the Ohms law power formulas.
The Power Triangle
and again, transposing the basic Ohms Law equation above for power gives us the following combinations
of the same equation to find the various individual quantities:
One other point about Power, if the calculated power is positive in value for any formula the component
absorbs the power, that is it is consuming or using power. But if the calculated power is negative in value the component
produces or generates power, in other words it is a source of electrical energy.
Also, we now know that the unit of power is the WATT, but some electrical devices such as
electric motors have a power rating in the old measurement of "Horsepower" or hp. The relationship between horsepower and
watts is given as: 1hp = 746W. So for example, a two-horsepower motor has a rating of 1492W,
(2 x 746) or 1.5kW.
Ohms Law Pie Chart
To help us understand the the relationship between the various values a little futher, we can take all
of Ohm's Law equations from above for finding Voltage, Current,
Resistance and Power and condense them into a simple
Ohms Law pie chart for use in AC and DC circuits and calculations as shown.
Ohms Law Pie Chart
As well as using the Ohm's Law Pie Chart shown above, we can also put the individual
Ohm's Law equations into a simple matrix table as shown for easy reference when calculating an unknown value.
Ohms Law Matrix Table
For the circuit shown below find the Voltage (V), the Current (I), the Resistance (R) and the Power (P).
Voltage [ V = I x R ] = 2 x 12Ω = 24V
Current [ I = V ÷ R ] = 24 ÷ 12Ω = 2A
Resistance [ R = V ÷ I ] = 24 ÷ 2 = 12 Ω
Power [ P = V x I ] = 24 x 2 = 48W
Power within an electrical circuit is only present when BOTH voltage and current are present
for example, In an Open-circuit condition, Voltage is present but there is no current flow I = 0
(zero), therefore V x 0 is 0 so the power dissipated within the circuit
must also be 0. Likewise, if we have a Short-circuit condition, current flow is present but there
is no voltage V = 0, therefore 0 x I = 0 so again the power dissipated
within the circuit is 0.
As electrical power is the product of V x I, the power dissipated in a circuit
is the same whether the circuit contains high voltage and low current or low voltage and high current flow. Generally, power
is dissipated in the form of Heat (heaters), Mechanical Work such as motors, etc Energy in the form
of radiated (Lamps) or as stored energy (Batteries).
Energy in Electrical Circuits
Electrical Energy that is either absorbed or produced is the product of the electrical power measured
in Watts and the time in Seconds with the unit of energy given as Watt-seconds or Joules.
Although electrical energy is measured in Joules it can become a very large value when used to calculate the
energy consumed by a component. For example, a single 100 W light bulb connected for one hour will consume a total of
100 watts x 3600 sec = 360,000 Joules. So prefixes such as kilojoules (kJ = 103J)
or megajoules (MJ = 106J) are used instead. If the electrical power is measured in
"kilowatts" and the time is given in hours then the unit of energy is in kilowatt-hours or kWh which
is commonly called a "Unit of Electricity" and is what consumers purchase from their electricity suppliers.
Now that we know what is the relationship between voltage, current and resistance in a circuit, in the next
tutorial about DC Theory we will look at the
Standard Electrical Units used in electrical
and electronic engineering to enable us to calculate these values and see that each value can be represented by either multiples
or sub-multiples of the unit.