Ohm's Law

Written by Jerry Ratzlaff. Posted in Electrical

Ohm's Law is the relationships between power \((P)\), voltage \((V)\), current \((I)\), and resistance \((R)\).


 pie chart

Voltage (Volt)

Volt \(\:(V)\:\) or \(\:(E)\:\) is a unit of electrical pressur. One volt is the amount of pressure that will cause one ampere of current in one ohm of resistance. Different voltages that are typically used in the oilfield in the USA are 480V, 4,160V and 12kV (Kilo Volt)


\(Volts = \sqrt{Watts \;\cdot\; Ohms}\;\; = \;\;V = \sqrt{P \;\cdot\; R}\)

\(Volts = \frac{Watts}{Amps}\;\; = \;\;V = \frac{P}{I}\)

\(Volts = Amps \;\cdot\; Ohms\;\; = \;\;V = I \;\cdot\; R\)

Current (Amp)

Current \(\:(I)\:\) is the rate of flow of electricity in a circuit, measured in amperes.

Amp is a unit of current. One ampere (amp) is the current flowing through one ohm of resistance at one volt potential.


\(Amps = \frac{Volts}{Ohms}\;\; = \;\;I = \frac{V}{R}\)

\(Amps = \frac{Watts}{Volts}\;\; = \;\;I = \frac{P}{V}\)

\(Amps = \sqrt{\frac{Watts}{Ohms}}\;\; = \;\;I = \sqrt{\frac{P}{R}}\)

Power (Watt)

Power \(\:(P)\:\) is the rate of doing work and is measured by the amount of foot pounds of work done in a particular unit of time. A horsepower is a measure of power.


\(Watts = \frac{Volts^2}{Ohms}\;\; = \;\;P = \frac{V^2}{R}\)

\(Watts = Volts^2 \;\cdot\; Ohms\;\; = \;\;P = V^2 \;\cdot\; R\)

\(Watts = Volts \;\cdot\; Amps\;\; = \;\;P = V \;\cdot\; I\)

Resistance (Ohm)

Resistance \(\:(R)\:\) is the ability to resist or prevent the flow of current. In order to overcome the resistance and get the current to flow a higher voltage will be required. Resistance is measured in Ohms, represented by \(R\) and has a symbols \(\Omega\).            

Ohm is a unit of resistance. A constant current of one ampere produces a force of one volt.


\(Ohms = \frac{Volts}{Amps}\;\; = \;\;R = \frac{V}{I}\)

\(Ohms = \frac{Volts^2}{Watts}\;\; = \;\;R = \frac{V^2}{P}\)

\(Ohms = \frac{Watts}{Amps^2}\;\; = \;\;R = \frac{P}{I^2}\)

electrical symbols

QuantitySymbolMeasuring UnitsDescription
Capacitance \(C\) Farad unit of capacitance

\(C=Q + V\)

Charge \(Q\) Coulomb unit of electrical charge

\(Q=C \cdot V\)

Conductance \(G\;\) Siemen reciprocal of resistance


Current \(I\) Amp unit of electrical current

\(I=V / R\)

Frequency \(Hz\) Hertz unit of frequency

\(f=1 + T\)

Impedance \(Z\) Ohm unit of AC resistance

\(Z^2=R^2 + X^2\)

Inductance \(L\;\) or \(\;H\) Volt unit of inductance

\(V_L=L (di / dt) \)

Power \(P\) Watt unit of power

\(P=V \cdot I\)

Resistance \(R\) or \(\Omega\) Ohm unit of DC resistance


Voltage \(V\;\) or \(\;E\) Volt unit of electrical potential

\(V=I \cdot R\)