Resistor

The resistor is one of the basic components in electrical circuits. Resistors are used where the resistance of the circuit needs adjustment, typically for limiting the electrical current between two nodes.

Function of resistors

The function of a resistor in a circuit is described by Ohm's law and dependends upon three variables: the resistance of the resistor, the voltage difference between its poles, and the flow of electrons (current) through the resistor. If two of the three are known, the third can easily be calculated.

Resistors are not polarized, meaning that they can be inserted into a circuit either way around.

Key properties of resistors

When choosing resistors for a circuit, parameters such as power rating, tolerance and temperature drift should be considered.

The physical size of the resistor component directly affects how much heat generation it can withstand before sustaining damage. The resistor must be selected such that its maximum power rating is not exceeded, however it is generally recommended to leave at least ten percent margin as well.

Resistors are specified with a nominal resistance value and a tolerance, often stated in percents. This tolerance states the maximum deviation of a single resistor from its nominal value. The resistance of two resistors are rarely precisely equal, but their values are both within a certain guaranteed interval, defined by the tolerance. Thus, resistors with low tolerance are often considered to be precision resistors.

As the ambient temperature of a resistor fluctuates, so does the resistance of the resistor. The amount by which the resistance fluctuates is known as the temperature drift, and is often stated in ppm/Celsius or ppm/Fahrenheit. Regular resistors experienced increased resistance with rising temperature, and vice versa. There are also NTC (Negative Temperature Coefficient) resistors, whose resistance decreases with rising temperature, and vice versa.

Combinations of resistors

Resistors may be combined either in series or in parallel, resulting in a total resistance dependent upon the individual resistances as well as the combination order.

Resistors in series

When connecting two or more resistors in series, the equivalent resistance becomes the sum of the individual resistances. Mathematically, this can be expressed as

$R_{\mathrm {eq} }=\sum _{n=1}^{N}R_{N}$

where $N$ is the number of resistors connected in series. If $N$ resistors with identical resistance $R$ are connected in series, the equivalent resistance becomes

$R_{\mathrm {eq} }=N\cdot R.$

Resistors in parallel

When two or more resistors are connected in parallel, the inverse of the equivalent resistance is equal to the sum of the inverses of the individual resistances. Mathematically, this is expressed as

${\frac {1}{R_{\mathrm {eq} }}}=\sum _{n=1}^{N}{\frac {1}{R_{n}}}$

where $N$ is the number of resistors connected in parallel. In the case of two resistors, the equivalent resistance can be calculated using the formula

$R_{\mathrm {eq} }={\frac {R_{1}\cdot R_{2}}{R_{1}+R_{2}}}.$

If $N$ resistors with identical resistance $R$ are connected in parallel, the equivalent resistance is

$R_{\mathrm {eq} }={\frac {R}{N}}.$

Calculation examples

This section contains some examples of how to calculate the operation of resistors.

Calculating current

If 10 volts of voltage is applied over a 100-ohm resistor, the current through the resistor will, according to Ohm's law, equal

$I={\frac {U}{R}}={\frac {10\ \mathrm {V} }{100\ \mathrm {ohm} }}=0.1\ \mathrm {A} =100\ \mathrm {mA} .$

Calculating voltage

If a current of 1 mA flows through a 1-kiloohm resistor, the voltage across the resistor becomes

$U=I\cdot R=0.001\ \mathrm {A} \cdot 1000\ \mathrm {ohm} =1\ \mathrm {V} .$

Calculating resistance

If a current of 50 mA flows through a resistor when 6 volts of voltage is applied, the resistance equals

$R={\frac {U}{I}}={\frac {6\ \mathrm {V} }{50\ \mathrm {mA} }}=120\ \mathrm {ohm} .$

Calculating equivalent resistance

If three resistors (R1 = 100 ohm, R2 = 200 ohm, R3 = 400 ohm) are connected in series, the equivalent resistance is

$R_{\mathrm {eq} }=R_{1}+R_{2}+R_{3}=100\ \mathrm {ohm} +200\ \mathrm {ohm} +400\ \mathrm {ohm} =700\ \mathrm {ohm} .$

If the same resistors are connected in parallel, the equivalent resistance is

${\frac {1}{R_{\mathrm {eq} }}}={\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+{\frac {1}{R_{3}}}={\frac {1}{100\ \mathrm {ohm} }}+{\frac {1}{200\ \mathrm {ohm} }}+{\frac {1}{400\ \mathrm {ohm} }}=0.0175\ {\frac {1}{\mathrm {ohm} }}.$

so

$R_{\mathrm {eq} }={\frac {1}{0.0175}}\ \mathrm {ohm} \approx 57\ \mathrm {ohm} .$