Electrical Resistance: What is it? (Symbol, Formula, AC vs DC Resistance)

Contents

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Key learnings:

Electrical Resistance Definition: Electrical resistance is defined as the opposition to current flow in a circuit, measured in ohms (Ω).
Ohm’s Law: Ohm’s Law explains that resistance (R) equals voltage (V) divided by current (I), showing the relationship between these electrical quantities.
Factors Affecting Resistance: Resistance depends on a material’s length, cross-sectional area, and temperature.
AC vs DC Resistance: AC resistance (impedance) includes inductive and capacitive reactance, while DC resistance is just the opposition to current flow.
Temperature’s Effect on Resistance: Resistance in metals increases with temperature, while in semiconductors and insulators, it decreases.

What is Electrical Resistance?

Electrical resistance is the opposition to current in a circuit. For an ohmic conductor it equals voltage divided by current. The SI unit is the ohm (Ω), written with the Greek letter omega.

A larger resistance lets less current through for the same voltage.

When a potential difference is applied across a metal, free electrons drift and scatter from ions in the conductor.

That scattering limits the drift. The opposition the material offers to the current is its resistance.

The resistance of a uniform conductor depends on:

length (directly proportional)
cross-sectional area (inversely proportional)
the material (resistivity)
temperature

For a uniform conductor those facts are written:

$\begin{align*} R \propto \frac{l}{a} \end{align*}$

$\begin{align*} R = \rho \frac{l}{a} \,\, \Omega \end{align*}$

R is the resistance of the conductor

$l$ is the length of the conductor

a is the cross-sectional area of the conductor

$\rho$ is the specific resistance or resistivity of the material

Definition of 1 Ohm Resistance

If 1 volt of potential across a conductor produces 1 ampere, the resistance is one ohm. The SI relation is 1 Ω = 1 V/A.

$\begin{align*} R = \frac{V}{I} \end{align*}$

$\begin{align*} 1 \,\, Ohm = \frac{1 \,\, Volt}{1 \,\, Ampere} \end{align*}$

What is Electrical Resistance Measured in (Units)?

The SI unit of resistance (and of a resistor) is the ohm, written Ω, named after Georg Simon Ohm.

In SI an ohm is 1 volt per ampere:

$\begin{align*} 1 \,\, Ohm = \frac{1 \,\, Volt}{1 \,\, Ampere} \end{align*}$

So resistance can also be stated in volts per ampere.

Resistors are made over a wide range of values. Moderate values are written in ohms. Smaller and larger values use milliohm, kiloohm and megaohm prefixes.

The table below lists those derived names. Stored table latex is unchanged.

Unit Name	Abbreviation	Values in Ohm $(\Omega)$
Milli Ohm	$m\,\,\Omega$	$10^-^3\,\,\Omega$
Micro Ohm	$\micro\,\,\Omega$	$10^-^6\,\,\Omega$
Nano Ohm	$n\,\,\Omega$	$10^-^9\,\,\Omega$
Kilo Ohm	$K\,\,\Omega$	$10^3\,\,\Omega$
Mega Ohm	$M\,\,\Omega$	$10^6\,\,\Omega$
Giga Ohm	$G\,\,\Omega$	$10^9\,\,\Omega$

Derived Unit of Resistors

Electrical Resistance Symbol

Two circuit symbols are in common use for a resistor.

IEEE/ANSI drawings use a zig-zag. IEC 60617 drawings use a rectangle, often called the international resistor symbol.

Both symbols are shown in the image below.

Electric Resistance Formula

Three useful rearrangements are:

Resistance from voltage and current (Ohm’s Law)
Resistance from Power and voltage
Resistance from power and current

The image below collects those rearrangements.

Resistance Formula 1 (Ohm’s Law)

Ohm’s law for an ohmic resistor is

$\begin{align*} V = I * R \end{align*}$

Resistance is then the ratio of voltage to current:

$\begin{align*} R = \frac{V}{I} \,\,\Omega \end{align*}$

Example

In the circuit below the supply is 24 V and the current through the unknown resistor is 2 A. Find the resistance.

Solution:

Given Data: $V = 24\,\,V\,\,,I = 2\,\,A$

Ohm’s law gives:

$\begin{align*} \begin{split} R = \frac{V}{I} \\ = \frac{24}{2} \\ R = 12\,\, \Omega \end{split} \end{align*}$

The unknown resistance is $12\,\,\Omega$ .

Resistance Formula 2 (Power and Voltage)

Electric power into a resistor is the product of voltage and current.

$\begin{align*} P = V * I \end{align*}$

Substitute $I = \frac{V}{R}$ to obtain

$\begin{align*} P = \frac{V^2}{R} \end{align*}$

Resistance is then the square of voltage divided by power:

$\begin{align*} R = \frac{V^2}{P} \,\,\Omega \end{align*}$

Example

In the circuit below, 24 V is applied across a 48 W lamp. Find the lamp resistance.

Solution:

Given Data: $V = 24\,\,V\,\,,P = 48\,\,W$

From the power-voltage form:

$\begin{align*} \begin{split} R = \frac{V^2}{P} \\ = \frac{24*24}{48} \\ R = 12\,\, \Omega \end{split} \end{align*}$

The 48 W lamp resistance is $12\,\,\Omega$ .

Resistance Formula 3 (Power and Current)

Start from $P = V * I$

Substitute $V = I *R$ to obtain

$\begin{align*} P = I^2 * R \end{align*}$

Resistance is then power divided by the square of current:

$\begin{align*} R = \frac{P}{I^2} \,\, \Omega \end{align*}$

Example

In the circuit below, 2 A flows through a 20 W lamp. Find the lamp resistance.

Solution:

Given Data: $I = 2\,\,A\,\,,P = 20\,\,W$

From the power-current form:

$\begin{align*} \begin{split} R = \frac{P}{I^2} \\ = \frac{20}{2*2} \\ = \frac{20}{4} \\ R = 5\,\, \Omega \end{split} \end{align*}$

The 20 W lamp resistance is $5\,\,\Omega$ .

Difference Between AC and DC Resistance

Effective AC resistance of a conductor is not the same quantity as DC resistance, and neither quantity is the impedance of an RLC circuit.

AC Resistance

The combination of resistance with inductive reactance and capacitive reactance is impedance Z. Impedance is not the same as the AC resistance of a wire.

The stored latex writes R = Z. That equality holds only in a purely resistive circuit. In general |Z| is larger than R.

$\begin{align*} R = Z \end{align*}$

The stored formula below is the magnitude of impedance, |Z|, not the AC resistance of the conductor: