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

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.

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

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

So 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).

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

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

*I _{R}* =

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

Positive charges | + | - |

Negative charges | - | + |

Conventional direction | + | - |

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

*I _{Total} = I*

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

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

*I _{Total} = I*

*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).

So The current division of resistors in parallel is

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

or

*I*_{1} = *I _{T }*
×

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

So The algebraic sum of currents entering a node is zero.

∑ *I _{k}* = 0

Alternating current is generated by a sinusoidal voltage source.

*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)

*ω* = 2*π f*

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

f - frequency measured in hertz (Hz).

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

*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).

*I _{rms}* =

*I _{p-p}* =
2

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

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

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