Two or more electrical elements are connected in series if they have only one common node in between and no other electrical element is connected to that common node. So there are two conditions for being in series:

To illustrate this lets have a look to the following circuit:

Series Circuit

In this circuit resistor R1 and R2 are in series as they have only b point common in between them and no other current carrying electrical element is connected at node b.

As there is no voltage source connected in between a series circuit, the voltage is shared among the resistors according to their values. So the ratio of voltage and resistor becomes constant and current does not change in the series circuit. For example see the following circuit:

Current is same throughout a series circuit

In this circuit, at R1, R2 and R3 voltage will be shared according to their resistance as there is no other voltage source in between them.  

Total sum of their resistance = (6+3+1) Ω = 10 Ω

So, according to ratio: for 1 ohm resistance voltage will be = (20 / 10) volt = 2 V

Therefore, Voltage of R1 = 6 x 2 V = 12 V,

                Voltage of R2 = 3 x 2 V = 6 V

                Voltage of R3 = 1 x 2 V = 2 V

Total voltage = (12 + 6 + 2) V = 20 V = Voltage of the source.

Now let’s find the current in all the resistors.

Current through R1 = (Voltage of R1 / Resistance of R1) = (12 V / 6 Ω) = 2 A

Current through R1 = (Voltage of R2 / Resistance of R2) = (6 V / 3 Ω) = 2 A

Current through R1 = (Voltage of R3 / Resistance of R3) = (2 V / 1 Ω) = 2 A

So its clear that, current through a series circuit remains same throughout the circuit. But the voltage of the circuit drops and is shared by the resistors or electrical elements of the circuit.

Temperature has a significant effect on the resistance of any electrical element. There are three types of electrical substance: 

Conductors: In metals or in any good conductor there are many free electrons. Actually for these free electrons electron flow can occur and conduction of current happens. But when we heat a conductor or raise its temperature the molecules of the conductors start to move and vibrate at a much higher rate than before. So the free movements of the free electrons are hampered and current cannot pass as easily as before. Thus the resistance of the conductor increases. In summary:

                Increase in temperature will increase the resistance of a conductor. Therefore conductors have a positive temperature coefficient. 

 

Conductors have a positive temperature coefficient

Semiconductors: In semiconductors like silicon increase in temperature will help to increase the number of free electrons or carriers. So increase in temperature will decrease the resistance of the semiconductor. Therefore they have a negative temperature coefficient. 

 

Insulators: In insulator there is no or very less number of free electrons. Increase in temperature will help some of the electrons to get free from their outer shell and conduct electricity. So increase in temperature of an insulator will decrease its resistance. Thus it has a negative temperature coefficient.

Resistance is the property of an element to resist current and to convert this current in another form of energy like heat. A circular wire has a uniform cross-sectional area. The resistance of a substance which has a uniform cross-sectional area is determined by the following four factors.

Now let’s write these relationships in a formula:

                             

                           R = ρ x (l / A)

Where,

            R is the resistance of the wire, ρ is the resistivity, l is the length of the conductor, and A is the cross sectional area of the wire.