Current and charges

​​In a nutshell

Current is defined as the rate of flow of charge which is an inherent property possessed by some particles and can be either positive or negative. Kirchhoff's first law states that at any point in an electrical circuit, the sum of the currents flowing into that point is equal to the sum of currents going out.

Equations

Constants

Variable definitions

Electric charge

The electric charge is an inherent physical property possessed by some particles such as electrons and protons. There are two types of charges known as positive and negative. Objects with opposite charges exert an attractive force on each other while objects with the same charge exert a repulsive force instead. Charge is measured in Coulombs $$C$$.

It is common to measure electrical charges relative to the elementary charge $$e$$ which is the charge of the proton ($$+1e$$) and the electron ($$-1e$$) and has a value of $$1.6\times10^{-19}\ C$$. Since the charge of most objects results from electrons being added (becoming more negative) or being taken away (becoming more positive), the net charge of an object can be written as multiples of $$e$$ as it is the smallest charge value:

$$Q=\pm ne$$​ 

Note: $$n$$ is the number of electrons.

Electric current

The electric current is defined as the rate of flow of charge and is measured in the SI base units amperes $$A$$ (or amps).  It can be found using the equation:

$$I=\dfrac{\Delta Q}{\Delta t}$$​​

Note: the $$\Delta$$ (delta) symbol represents the change in a variable.

Example

A charge of $$12\ C$$ passes through a wire for $$6\ s$$, calculate the current in the wire.

Firstly, write down all the known values:

$$\Delta Q= 12\ C\newline \Delta t=6\ s$$​​

Next, write down the equation:

$$I=\dfrac{\Delta Q}{\Delta t}$$

Substitute all the values into the equation:

$$I=\dfrac{12}{6}$$​​

Calculate the value:

$$I=2\ A$$​​

The wire has a current of $$\underline{2\ A}$$.

Kirchhoff's first law

One of the fundamental laws of physics is the conservation of charge, which states that charge can never be created nor destroyed. This results in Kirchhoff's first law which states that at any point in an electric circuit, the sum of the currents going into that point is equal to the sum of the currents going out. It can be represented as:

$$\Sigma I_{in}=\Sigma I_{out}$$​​

Note: $$\Sigma$$ (sigma) denotes the sum of the variables.

Kirchhoff's first law is more easily visualized through circuit diagrams:

Example

What is the value of the current $$x$$?

Firstly, identify which currents are going into the point P and which are going out:

​$$\begin{aligned}I_{in}&=7\ A \\ I_{out}&= 15\ A \\ I_{in}&=x\end{aligned}$$​​

Next, write down the equation:

​$$\Sigma I_{in}=\Sigma I_{out}$$​​

Substitute all the values into the equation:

$$7\ + x=15\$$​​

Rearrange to find $$x$$:

​$$x=15-7$$​​

Calculate the value:

$$x=8\ A$$​​

The value of the current $$x$$ is $$\underline{8\ A}$$.