In 1827, George Simon Ohm, a German physicist, published a paper titled, “The Galvanic Circuit Investigated Mathematically.” Here, Ohm described a series of experiments in which he measured and analyzed current and voltage through and across various conductive materials. He concluded that in certain materials, current and voltage were directly proportional, related by a constant, resistance, the unit of which is the ohm (Ω).

### Ohm's Law

According to Ohm’s law, the voltage *V* across a current-carrying resistor is the product of the current *I* and resistance *R; V = RI*. The corresponding power *P* dissipated by the resistor is found by substituting *V = RI* in the standard power equation *P= VI*, yielding *P = (RI)I = I ^{2}R.*

### Resistors at work

A resistor is an electrical component often used to limit current or reduce source voltage powering a load. Industrial applications for resistors — big, tough ones — are quite common, running the gamut from dynamic braking on adjustable-speed drives to reducedvoltage (soft) starting on ac motor-driven conveyors, hoists, pumps, and mill stands. They also include current or torque-limited starting and stopping on equipment powered by dc motors.

### Series connection

The equivalent resistance *R _{Es}* of two or more resistors connected in series is the sum of the individual resistances.

*R _{Es} = R_{1s} + R_{2s} + ... R_{Ns}*

### Parallel connection

The equivalent resistance REp of two or more resistors connected in parallel is the reciprocal of the sum of the reciprocals of each resistance.

*R _{Ep} = 1/(1/R_{1p} + 1/R_{2p} + ... 1/R_{Np})*