Resistance in Series/Parallel Connection

Resistance in Series:-

More than one resistances can be connected either in series or in parallel connections. Now if we connect two resistances end on end then they are said to be connected in series. 

Let's take an example:

Consider three resistances R1, R2 and R3 be connected in series as shown below:

                                        
Now Equivalent resistance of this circuit equals to the sum of individual resistances,let's prove it now:
In series circuit
(1) Same current flows through each resistance.
(2) Voltage drop across each resistance is different.
(3) Net voltage drop applied across circuit equals the sum of all voltage drops across each resistance

Therefore Vs= V1 + V2 + V3 = IR1 + IR2 + IR3

Since Vs= IR 
(R is the equivalent resistance of circuit)

Then      IR = IR1 + IR2 + IR3
              IR = I (R1+R2+R3)
Cancelling out I from both sides we get

                  R = R1 + R2 + R3

Resistances in Parallel:-

As shown In below figure Resistances are said to be connected in Parallel connection.

                                 
In parallel circuit 
(1) Potential difference across all resistances is same.
(2) Current flowing through each resistance is different.
(3) Net current flowing through circuit is sum of three currents.


             I = t1 + t2 + t3  = V/r1 + V/r2 + V/r3

             Also I = V/R
where V is the voltage applied and R is the equivalent resistance of circuit

              So V/R =  V/r1 + V/r2 + V/r3

                    1/R = 1/r1 + 1/r2 + 1/r3