Electric Current: What is it? (Formula, Units, AC vs DC)

Contents

💡

Key learnings:

Electric Current Definition: Electric current is defined as the flow of charged particles—such as electrons or ions—through a conductor or space.
Electric Current Formula: The flow rate of electric charge is calculated by dividing the change in charge by the change in time.
Electric Current Units: The SI unit for current is the ampere (A), representing 1 coulomb of charge passing a point in 1 second.
AC vs DC Current: Alternating current (AC) periodically reverses direction, while direct current (DC) flows in one direction.
Current Measurement: Current is measured using devices like ammeters and galvanometers.

What is Electric Current?

Electric current is the net flow of charged particles (electrons, ions or holes) through a conductor or through space. Instantaneous current is how fast electric charge passes a surface: I = dQ/dt. Circuit symbols are I or i. The SI unit is the ampere (A).

In symbols,

$\begin{align*} I = \frac {dQ} {dt} \end{align*}$

The moving particles in an electrical conductor or in space are the charge carriers: electrons, holes or ions, depending on the medium.

Which carriers move depends on the medium:

In a metal, the carriers are electrons.
In semiconductors, electrons and holes both contribute.
In an electrolyte, the carriers are ions.
In a plasma (ionized gas), ions and electrons both move.

A voltage or potential difference across a closed path drives conventional current from the higher-potential node toward the lower. For a given ohmic resistance, larger voltage means larger current.

Equal potentials at two nodes means no current through a resistor joining them. In many circuits current is the result of voltage. Independent current sources and superconductors are exceptions to that slogan.

A current produces a magnetic field, which inductors, transformers, generators and motors use. In a resistive conductor the same current produces heating (I²R, joule heating), which is how an incandescent lamp makes light.

A time-varying current (and its associated fields) can radiate electromagnetic waves, which radio and other links use to carry information.

AC vs DC Current

By time behaviour, current is grouped as alternating current (AC) or direct current (DC).

AC Current

Alternating current reverses direction on a repeating cycle. “AC current” repeats the word current. Use AC or alternating current.

The polarity of i(t) changes at the waveform period (50 Hz or 60 Hz on utility mains).

A sine-wave AC starts at zero, rises to a peak, returns through zero then reaches the opposite peak and repeats.

The repeating wave can be sinusoidal, triangular, square or sawtooth.

What makes it AC is the periodic reversal (or zero-mean oscillation), not the exact shape.

Mains and most rotating machines produce a sine wave, as in the figure below.

An alternator (synchronous generator) is built to produce AC.

Utility supply to homes and industry is AC, mainly because transformers change voltage efficiently.

DC Current

Direct current does not reverse. “DC current” repeats the word current. Use DC or direct current. Steady DC is constant. Pulsating DC stays one polarity but its magnitude varies.

Unidirectional is another name for that one-way flow. A constant DC trace is below.

Sources include batteries, solar cells, fuel cells, thermocouples and commutator DC machines. A rectifier turns AC into DC (often with ripple unless filtered).

Electronics usually run from DC rails. HVDC transmission is the high-voltage exception: DC used at hundreds of kilovolts.

What is Electric Current Measured In (Current Units)?

The SI unit is the ampere (symbol A), a base unit, named for André-Marie Ampère.

One ampere is one coulomb per second (the coulomb is defined from the ampere: 1 C = 1 A·s). Since the 2019 SI revision the ampere is fixed by the elementary charge e, not by the old force-between-two-wires experiment. The 1 C/s relation still holds.

$\begin{align*} 1 \,\, Ampere = \frac {1\,\,Coulomb} {1\,\,Second} = \frac {C} {S} \end{align*}$

So A and C/s are the same quantity. Write C/s, not C/S (S is siemens).

Electric Current Formula

Circuit formulas (ohmic / DC or RMS on a resistor):

I = V/R from Ohm’s Law
I = P/V when P = V I
I = √(P/R) when P = I²R

The same Ohm’s-law triangle is below. They do not replace I = dQ/dt.

current formula traingle — Current Formula Triangle

Current Formula 1 (Ohm’s Law)

Ohm’s law:

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

Thus,

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

Example

A supply of $24\,\,V$ is across a $12\,\,\Omega$ resistance. Find the current in the resistor.

Solution:

Given: $V=24\,\,V ,\,\, R=12\,\,\Omega$

Ohm’s law:

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

The current is $2\,\,A$ .

Current Formula 2 (Power and Voltage)

For DC (or average on a resistor), electrical power is P = V I.

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

So I = P/V when that product applies:

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

Here $A$ means amperes.

Example

A $24\,\,V$ supply feeds a $48\,\,W$ lamp. Find the current taken by the $48\,\,W$ lamp, treating P = V I as valid at that operating point.

Solution:

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

From I = P/V,

$\begin{align*} & I = \frac{P}{V} \\ & = \frac{48}{24} \\ & I = 2\,\,A \end{align*}$

The $48\,\,W$ lamp then draws $2\,\,A$ .

Current Formula 3 (Power and Resistance, Ohmic Loss, Resistive Heating)

Start from $P = V * I$

Put Ohm’s law $V = I * R$ into that product:

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

Then I = √(P/R) for a positive DC (or RMS) value:

$\begin{align*} I = \sqrt{\frac{P}{R}}\,\,A \end{align*}$

Example

Find the current in a $100\,\,W$ , $20\,\,\Omega$ lamp using I = √(P/R).

Solution:

Given: $P=100\,\,W ,\,\, R=20\,\,\Omega$

Then

$\begin{align*} & I = \sqrt{\frac{P}{R}} \\ & = \sqrt{\frac{100}{20}} \\ & = \sqrt{5} \\ & I = 2.24\,\,A \end{align*}$

For that $100\,\,W$ , $20\,\,\Omega$ lamp, √5 ≈ 2.236 so the current is $2.24\,\,A$ .

Dimensions of Current

If charge Q is taken as a dimension, I is $M^0L^0T^-^1Q$ (that is Q/T). In SI, current is a base unit, so the dimension is I (or A), and charge is I T.

Current is coulomb per second, so

$\begin{align*} I = \frac{Q}{t} = \frac{[Q]}{[T]} = QT^-^1 = M^0L^0T^-^1Q \end{align*}$

Conventional Current vs Electron Flow

Circuit diagrams use conventional current. Metals actually move electrons the other way.

In metals the mobile carriers are free electrons. An electric field is defined as the force per unit positive test charge, so electrons (negative) drift against E.

A voltage across a closed metallic path makes those electrons drift, which is a current.

Conventional current in the external circuit is drawn from the battery positive toward the battery negative, the direction a positive test charge would move.

In a metal the ion lattice stays put and electrons move. In a semiconductor both electrons and holes can contribute.

Positive carriers one way, or negative carriers the opposite way, give the same current sign. Circuits therefore pick one arrow: conventional current, independent of which carrier is moving.

Conventional current is the positive-carrier direction: higher potential to lower. Electrons drift from lower potential to higher. The two arrows are opposite, as in the figure below.

direction of coventional current and electron flow — The Direction of Conventional Current and Electron Flow

In short:

Conventional Current: the positive-carrier arrow, from battery + through the load to battery −.
Electron Flow: electrons drift from battery − through the load to battery +. Opposite to the conventional arrow.

The same directions on a battery circuit:

conventional current flow and electron flow — Conventional Current Flow and Electron Flow

Convection Current vs Conduction Flow

Convection Current

A convection current here means charge transported through an insulating medium (liquid, gas or vacuum), not bound to a metal lattice. (In fluids, “convection” also means bulk motion of the medium.)

That path is not an ohmic metal, so it need not obey Ohm’s law. A vacuum tube is the usual example: electrons leave the cathode and cross the vacuum to the anode.

Conduction Current

Conduction current is charge drift in a material (metal, electrolyte, semiconductor). Ohm’s law holds only for ohmic materials over the stated range, not for every conductor.

Displacement Current

A resistor and a capacitor in parallel on source V (figure below) carry different kinds of current.

The resistor current, while V is applied, is

$\begin{align*} I_1 = \frac{V}{R} \end{align*}$

That is “conduction current.”

The capacitor branch current is nonzero only while its voltage is changing:

$\begin{align*} I_2 = \frac{dQ}{dt} = C \frac{dV}{dt} \end{align*}$

Maxwell called the ε dΦ_E/dt term “displacement current.”

No conduction charge crosses the ideal dielectric gap. Displacement current is still a real term in the Ampere-Maxwell law: it makes the magnetic field around a charging capacitor continuous with the conduction current in the wires.

How To Measure Current

Measuring current tells you load, heating and protection settings.

An ammeter reads current. Connect it in series with the path you want, never across the supply like a voltmeter.

A series ammeter on a resistor is shown below.

current measurement by ammeter method — Measurement of a Current by an Ammeter

A galvanometer is a sensitive current detector. It shows polarity (direction) and a deflection related to current. A tangent galvanometer can be used as an absolute instrument (current from geometry and the Earth’s field). An ordinary panel meter is not that.

Clamp and Hall sensors read the magnetic field of the current so you need not open the conductor. Examples:

Hall effect current sensor transducers
Current transformer (CT) (ordinary iron CTs measure AC; DC needs a Hall or fluxgate CT)
Clamp meters
Shunt resistors
Magneto resistive field sensors

Common Questions About Current

Short answers to common questions:

What Uses an Electromagnet to Measure Electric Current?

A moving-coil galvanometer uses a coil in a magnetic field (an electromagnet arrangement) so current in the coil produces torque.

A tangent galvanometer is the absolute type: I is found from the tangent of the deflection and the coil constants. Most galvanometers are secondary instruments, calibrated against a standard.

Inserting it still means opening the circuit, which is often inconvenient. Use a clamp meter or a shunt already in the panel when you cannot break the run.

How Does an Electric Current Produce a Magnetic Force?

A current-carrying conductor in a magnetic field feels a force F = I ℓ × B (charges moving in B).

Figure (a) is a wire with current. The field around the wire follows the right-hand grip rule (thumb along conventional current, fingers curl in B). Fleming’s right-hand rule is the generator rule (induced current). The motor force on the wire uses Fleming’s left-hand rule.

magnetic force produced by an electric current — Magnetic Force Produced by an Electric Current

If an external field is left-to-right, the wire’s own field strengthens B on one side and weakens it on the other (the stored “waken” is weaken).

The unbalanced field then pushes the wire as in figure (b). Use F = B I ℓ sinθ (stored) with the left-hand motor rule for direction.

Magnitude of that force:

$\begin{align*} F_B = BIL\,\,Sin\theta \end{align*}$

To Make an Electric Current Flow, It Is Necessary to Have

A sustained current in a simple loop needs:

A potential difference between two points of the path (equal potentials give no current in a resistor)
A voltage source or current source (battery, cell, supply) to drive the carriers
A conducting path for the carriers
A closed loop for DC. (A capacitor still passes AC via displacement current.)

A closed loop with a source is shown below. Displacement current in a capacitor still lets AC “flow” in a circuit that looks open to DC.

current flowing in a closed circuit — Current Flowing in a Closed Circuit

Which Best Describes a Difference Between Electric Current and Static Electricity

Current is charge in motion through a path. Static electricity is charge sitting on a body (or jumping once as a spark).

Those static charges rest on a surface until they leak or discharge.

Current in metals is electron drift. Static charging is charge transfer between objects (electrons or ions), after which the net charge may sit still.

A continuous current needs a closed conducting path (or a displacement path). Charge can accumulate on conductors and on insulators.

How Does an Electric Current Affect a Magnetic Pole?

Moving charge produces B. A magnetic dipole in that B feels a torque and, in a nonuniform field, a force.

Like magnetic poles repel; unlike poles attract. That is magnetism, not a special current rule. The current’s B field is what pushes or twists a nearby magnet.

What Instrument Is Used to Measure Electric Current

An ammeter still belongs in series with the unknown current.

Other tools (some already listed):

Hall effect current sensor transducers
Current transformer (CT) (AC on a standard CT)
Clamp-on meters
Shunt resistors
Magnetoresistive field sensors