Equivalent resistance is the single resistance value that can replace a combination of resistors in a circuit without altering the circuit's overall behavior. It represents the total resistance that produces the same effect on current flow as the combined resistors.
The word "equivalent" comes from the Latin aequivalens, which means "of equal worth." It combines aequi- (equal) and valens (worth or strength).
In mathematics, the term "equal" is commonly used, e.g., "5 + 5 is equivalent to 10." In this basic mathematical calculation, the result of 5+5 is equal to 10 in value.
In electronics engineering and science, the calculation of equivalent resistance is used to determine the total resistance value of a number of resistors connected in series. For example, a 5 Ω resistor connected in series with a 10Ω resistor results in an equivalent resistance of 15 (5+10=15).
It can also be used to calculate the resistance of resistors connected in parallel. For instance, two 10Ω resistors connected in parallel result in an equivalent resistance of 5 Ω (1/(1/10+1/10)=5).
Two equivalent resistors have identical resistive values.
In sensors and measurement circuits, equivalent resistors are utilized to balance resistances in Wheatstone bridges.
In thermal management, the concept of equivalent resistors is used to calculate power dissipation in resistors by employing an equivalent resistance.
An example of practical use that combines thermal management and sensor circuits is a heat loss vacuum sensor, commonly known as a Pirani vacuum gauge. In a Pirani vacuum gauge, a heated wire with a high temperature coefficient is maintained at a target temperature by keeping the sensor wire resistance equivalent to the resistive value of a fixed reference resistor. This operational principle of the Pirani gauge was described by Marcello S. Pirani in 1906.
References
- Introduction to Electric Circuits, 9th edition, 2013, James A. Svoboda, Richard C. Dorf
- Selbstzeigendes Vakuum - Messinstruments; Marcello S. Pirani, 1906, Deutsche Physikalische Gesellschaft, Verh.24(8): 686–694.
