Ohm's Law.

Fundamental Series FS01 - September, 2005

Ohm's Law defines the relationships between (V) voltage, (I) current, and (R) resistance. It states:

I = V ÷ R

Notes:

Biography and Backgound

George Simon Ohm, was born March16,1789 in Erlangen, Bavaria, Germany. Georg’s father, Johann, though self-taught, educated his sons Georg and Martin, to doctoral-levels in mathematics, physics, chemistry and philosophy. Georg continued his private studies and experiments throughout life.

A pioneer in the concise mathematical foundation of Physics, which up to his time was mostly descriptive and annecdotal in nature, his early studies and experiments led him to make the statement; I feel clearly that only that which is simple can be great.

In Ohm’s time, voltage and current were considered to be separate entities. His experiments and observations helped him to simplify and demystify the relationship between current, electromotive force, and resistance, and formulate what is now know as Ohm’s Law.

Ohm’s law states:

The flow of current is directly proportional to voltage and inversely proportional to resistance.

Mathematically expressed as:

I = V ÷ R

from wich it follows:

R = V ÷ I

Which is the mathematical definition of the fundemental electrical property of Resistance.

Always in quest for an appointment as a university department head, Goerg’s life-long pursuit was finally achieved late in his life in 1852 when he was appointed to the chair of physics at the University of Munich.

On July 7, 1854, Georg Ohm passed away in Munich at the age of 65.

His ultimate honor came after his death in 1881 when the Electrical Congress in Paris voted to adopt the ‘Ohm’ as the international standard of electrical resistance.

A Voltage (V) of One Volt applied across a resistance (R) of one Ohm will maintain current (I) of one Ampere.

Ohm, Georg Simon (1787-1854)

Ohm's law applications:

Ohm's Law expreses the relationship between Voltage (V), Current (I) and Resistance (R). If you know two of the variables, the the third can be readily calculated as follow:

V = I x R
I = V ÷ R
R = V ÷ I

V = I x R
I = V ÷ R
R = V ÷ I

An important application Ohm's Law is Power calculation. The unit of power is the Watt (W). At any instant of time instantaneous Power (P) is product of Current (I) times Voltage (E)

P = V x I W

From Ohm's Law we can restate this relationship using Resistance and Voltage

P = V x (V ÷ R)
or,
P = V ² ÷ R

Similarly from Ohm's Law we can calculate power using Resistance and Current

P = (I x R) X I
or,
P = I ² x R

One common mistake is to confuse instantaneous power with average power. Average power is the effective power dissipated over a cycle of time.

P_avg = V_avg x I_avg

In the case of a constant current, voltage, and resistance, instantaneous power and average power are the same.

Finally, it should be noted if voltage or current are time-varing, calculation of average power is more complicated. For example common household voltage in the US is a 60-Hz sinsusoid, or AC Voltage. In a complete cycle, its value will go from 0-V to a +V_peak to 0-V to -V_peak back to 0-V.

You might ask, "can we approximate the AC waveform with an equivalent unvarying or DC (Direct current) Voltage to simplify the problem so we can apply Ohm's Law like we do above?"

Yes we can! One method commonly used is the root-mean-square or RMS measurement of the waveform. Sometimes called the effective value, the RMS value is equivalent to value of a DC waveform delivering the same power. The equation to calculate RMS is straight forward, athough a bit complex to solve depending upon the waveform.

Where f(t) is the wave form function, and T is the length of one period of the waveform in seconds.

Just as reality check, for DC waveforms, f(t) = V and is time independent so the solution of the above equation is

A_rms = sqrt[1÷T x ( V ² [T-0] )

which reduces to

A_rms = V

Which is what we would expect - the effective value of a DC voltage is the DC voltage. If the reader takes the time to solve the same equation for a sinusoidal waveform, they would find for an AC sinusoidal waveform, A_o:

A_rms = 0.707A_o

For example, 115-V, 60-Hz household voltage is really a sinusoidal waveform of peak amplitude 163-V, and a RMS value of 115V - which we use for our household power calculations.

In conclusion

These are only just a few examples of applications of Ohm's Law. Ohm's law is probably the first thing most electrical engineering students learn because it fundamental to understanding and analyzing circuit and networks no matter how complex.