## Electric Current

Electric current definition and calculations.

- Electric current definition
- Electric current calculation
- Current calculation with Ohm's law
- Current in series circuits
- Current in parallel circuits
- Current divider
- Kirchhoff's current law
- Alternating Current (AC)
- Current measurement

### Electric current definition

Electrical current is the flow rate of electric charge in electric field, usually in electrical circuit.

Using water pipe analogy, we can visualize the electrical current as water current that flows in a pipe.

The electrical current is measured in ampere (amp) unit.

### Electric current calculation

Electrical current is measured by the rate of electric charge flow in an electrical circuit:

*i*(*t*) = *dQ(t) */* dt*

The momentary current is given by the derivative of the electric charge by time.

i(t) is the momentary current *I* at time t in amps (A).

Q(t) is the momentary electric charge in coulombs (C).

t is the time in seconds (s).

When the current is constant:

*I* = Δ*Q* / Δ
*t*

I is the current in amps (A).

ΔQ is the electric charge in coulombs (C), that flows at time duration of Δt.

Δt is the time duration in seconds (s).

##### Example

When 5 coulombs flow through a resistor for duration of 10 seconds,

the current will be calculated by:

*I* = Δ*Q* / Δ
*t * = 5C / 10s = 0.5A

### Current calculation with Ohm's law

The current *I _{R }*in anps (A) is equal to the resistor's voltage

*V*in volts (V) divided by the resistance

_{R }*R*in ohms (Ω).

*I _{R}* =

*V*/

_{R}*R*

##### Current direction

current type | from | to |
---|---|---|

Positive charges | + | - |

Negative charges | - | + |

Conventional direction | + | - |

### Current in series circuits

Current that flows through resistors in series is equal in all resistors - just like water flow through a single pipe.

*I _{Total} = I*

_{1 }=

*I*

_{2 }=

*I*

_{3 }=...

*I _{Total}* - the equivalent current in amps (A).

*I*_{1} - current of load #1 in amps (A).

*I*_{2} - current of load #2 in amps (A).

*I*_{3} - current of load #3 in amps (A).

### Current in parallel circuits

Current that flows through loads in parallel - just like water flow through parallel pipes.

The total current *I _{Total}* is the sum of the parallel currents of each load:

*I _{Total} = I*

_{1 }+

*I*

_{2 }+

*I*

_{3 }+...

*I _{Total}* - the equivalent current in amps (A).

*I*_{1} - current of load #1 in amps (A).

*I*_{2} - current of load #2 in amps (A).

*I*_{3} - current of load #3 in amps (A).

### Current divider

The current division of resistors in parallel is

*R _{T}* = 1 / (1/

*R*

_{2}+ 1/

*R*

_{3})

or

*I*_{1} = *I _{T }* ×

*R*/ (

_{T}*R*

_{1}+

*R*)

_{T}### Kirchhoff's current law (KCL)

The junction of several electrical components is called a *node*.

The algebraic sum of currents entering a node is zero.

∑ *I _{k}* = 0

### Alternating Current (AC)

Alternating current is generated by a sinusoidal voltage source.

##### Ohm's law

*I*_{Z} =
*V*_{Z} / *Z*

*I*_{Z} - current flow through the load measured in amperes (A)

*V*_{Z} - voltage drop on the load measured in volts (V)

*Z* - impedance of the load measured in ohms (Ω)

##### Angular frequency

*ω* = 2*π f*

ω - angular velocity measured in radians per second (rad/s)

f - frequency measured in hertz (Hz).

##### Momentary current

*i*(*t*) = *I _{peak}*

*sin*(

*ωt+θ*)

*i*(*t*) - momentary current at time t, measured in amps (A).

Ipeak - maximal current (=amplitude of sine), measured in amps (A).

*ω - *angular frequency measured in radians per second (rad/s).

t - time, measured in seconds (s).

*θ* - phase of sine wave in radians (rad).

##### RMS (effective) current

*I _{rms}* =

*I*

_{eff}=

*I*

_{peak }/ √2 ≈ 0.707

*I*

_{peak}

##### Peak-to-peak current

*I _{p-p}* = 2

*I*

_{peak}

### Current measurement

Current measurement is done by connecting the ammeter in series to the measured object, so all the measured current will flow through the ammeter.

The ammeter has very low resistance, so it almost does not affect the measured circuit.