Current

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

Electric current (German: elektrische Stromstärke, also Strom) is also simply called current.
It indicates how many charge carriers (here: electrons) flow through the cross-section of a conductor (e.g. a cable) per unit of time (here: second).

1 Quantity symbol and unit

The quantity symbol of electric current is $I$.
Its dimension (unit) is the ampere, named after André-Marie Ampère, and it is abbreviated with the unit symbol A.

$$[I]=\mathrm{A}$$

(read: ‘The dimension of $I$ is the ampere.’)

The ampere is one of the SI base units. In the International System of Units (SI), one ampere corresponds to a current of $1\mathrm{C}$ (coulomb), i.e. approx. $6.242\cdot 10^{18}$ elementary charges (just over 6 quintillion electrons) per second through a conductor cross-section.

The capital letter $I$ stands for a constant direct current or the constant mean value of a time-dependent alternating current.

To denote a time-dependent current, the lower-case letter $i=i(t)$ is used for the instantaneous value of the current. This is used, for example, when charging and discharging capacitors or capacitances, when switching inductors or inductances on and off, and with alternating current.

In complex AC calculation, the quantity symbol $\underline{I}$ is used for the current as a complex quantity.

2 Practical and worked examples

The current results from the number of charge carriers that pass a defined cross-section in a certain time:

$$I=\frac{Q}{t}$$

2.1 Current through an incandescent bulb

The current that flows from a battery through an incandescent bulb is stated, for example, like this:

$$I=0.2\mathrm{A}=200\mathrm{mA}$$

2.2 Charging current of a capacitor

The formula for the current when charging a capacitor via a resistor is, for example:

$$i(t)=I_0\cdot e^{-\frac{t}{RC}}$$

where:

• $i(t)$ the current as a function of time
• $I_0$ the initial current
• $e$ Euler’s number ($e\approx 2.71828$)
• $t$ the time as the function variable
• $R$ the resistance connected in series with the capacitor
• $C$ the capacitance of the capacitor

This formula describes the exponential decrease of the current during the charging process of a capacitance. Once the capacitor is full (in practice after five times the time constant $5\cdot \tau =5\cdot \mathrm{R}\cdot \mathrm{C}$), no charging current flows any more. In a DC circuit, the capacitor acts like an interruption once five times the time constant has elapsed.

2.3 Mains current

The mains current that comes from the socket-outlet is written like this:

$$i(t)=\hat{i}\cdot \sin (\omega t)$$

where:

• $i(t)$ the instantaneous current as a function of time
• $\hat{i}$ the peak value (the amplitude) of the current
• $\omega$ the angular frequency: $\omega =2\cdot \pi \cdot f$, where:
  • $\pi$ the circle constant, $\pi \approx 3.14159$
  • f the frequency, here: 50 Hz
  • here: $\omega =2\pi f\approx 314{\mathrm{s}}^{-1}$
• $t$ the time

This formula describes the sinusoidal waveform of the alternating current that can be drawn from the power grid by a resistive load, e.g. an incandescent bulb or a heating device.

3 Typical orders of magnitude

While the base current of a bipolar transistor can amount to a few microamperes ($\mu \mathrm{A}=10^{-6}\mathrm{A}=0.000001\mathrm{A}$) or less, it is not unusual for several hundred kiloamperes ($\mathrm{kA}=10^3\mathrm{A}=1000\mathrm{A}$) to flow through the electric lines in the networks of energy suppliers.

4 Example phrasings

• ‘A current of $8.7\mathrm{A}$ flows through the supply cable of the fan heater.’
• ‘The miniature fuse trips when the current exceeds $500\mathrm{mA}$.’
• ‘The series resistor is designed so that a current of $15\mathrm{mA}$ flows through the light emitting diode.’
• ‘The maximum permissible current through a commercially available extension lead is $16\mathrm{A}$.’

5 Related quantities

• Current and voltage across a resistor are proportional to each other. Together with the voltage and the resistance, the current therefore appears in the formula of Ohm’s law:

$$I=\frac{U}{R}$$

• The current is the quotient of electric power and voltage.

$$I=\frac{P}{U}$$

• Relation to electric charge and time:

$$Q=I\cdot t$$

(for constant current)

• The current density is the quotient of the current and the cross-sectional area through which the current flows:

$$J=\frac{I}{A}$$

6 Relevant components

In most applications, current flows through all components of an electric circuit.
For the design (dimensioning) of these components, the current plays a particularly important role:

• Conductor
• Resistor
• Switch
• Relay and contactor
• Battery and rechargeable battery
• Capacitor
• Inductor

To measure the current, the multimeter is used.