Resistance in Series and Parallel - Definition, Unit, Formula, Difference

•Resistances in Series

Suppose, three resistors, R1, R2 and R3 and you connect them end to end as shown in the figure

below, then it would be referred as resistances in series.

Resistance between point A and D in the figure below is equal to the sum of three individual

resistances. The current enters in to the point A of the combination, will also leave from point D as there is

no other parallel path provided in the circuit.

Now say this current is I. So this current I will pass through the resistance R1 R2 and R3. Applying Ohms law, it can be found that voltage drops across the resistances will be V1 = IR1 & V2 = IR2 and 3= IR 

Now, if total voltage applied across the combination of resistances in series, is V.

Then obviously

Since, sum of voltage drops across the individual resistance is nothing but the equal to applied voltage across the combination.

Now, ifwe consider the total combination of resistances as a single resistor of electric resistance value R then according to Ohm's law:-

Now, comparing equation (1) and (2), we get so, the above proof shows that equivalent resistance of a combination of resistances in series is equal to the sum of individual resistance. 

If there were n number of resistances instead of three resistances, the equivalent resistance will be

• Resistances in Parallel

Let's three resistors ofresistance value R1, R2 and R3 are connected in such a manner, that right side terminal of each resistor are connected together as shown in the figure below, and also left side terminal of each resistor are also connected together.

This combination is called resistances in parallel

If electric potential difference is applied across this combination, then it will draw a current I(say).As this current will get three parallel paths through these three electrical resistances, the current will be divided into three parts. Say currents Iı, I1 and I1 pass through resistor R1, R2 and R3 respectively. Where

total source current

I=I1+I2+I3...............1.

Now, as from the figure it is clear that, each of the resistances in parallel, is connected, across the same voltage source, the voltage drops across each resistor is same, and it is same as supply voltage V (say).

Hence,according to Ohm's law,

Now, if we consider the equivalent resistance of the combination is R. Then,

Now putting the values of I, Iı, I2 and I3 in equation (1) we get,

so, the final Formula for Resistance in Parallel is as follows