Resistance in series
Suppose a circuit connected in series as shown in fig above and has a resistance at different section are R1, R2, and R3.
Let current I flow through the network and voltage across resistance R1, R2 and R3 are V1, V2, and V3 respectively.
According to ohms law
V=I*R..........(i)
From the circuit
V= V1+V2+V3..........(ii)
Or, V = IR1 + IR2 + IR3..........(iii)
Or, V = I (R1 + R2 + R3).........(iv)
From equation (i) and (iv)
IR = I (R1 + R2 + R3)..........(v)
Or, R = R1 + R2 + R3
Hence equivalent resistance in the series circuit is the sum of all resistance which is connected.
From above criteria, some characteristics are obtained for resistance in series.
1. The same current flowing through the circuit.
2. Voltage drop for different resistance is different.
Resistance in parallel
Suppose a circuit connected in parallel with resistance as shown in fig above and has a resistance at different parallel section are R1, R2, and R3.
Let voltage V applied to the network and current flowing through the resistance R1, R2 and R3 are I1, I2, and I3 respectively.
According to ohms law
V=I*R..........(i)
From the circuit
I = I1 + I2 + I3..........(ii)
Or, I = V/R1 + V/ R2 + V/R3..........(iii)
Or, I = V(1/R1 + 1/ R2 + 1/R3)..........(iv)
From equation (i) and (iv)
V/R = V(1/R1 + 1/ R2 + 1/R3)..........(V)
Or, R= 1/R1 + 1/ R2 + 1/R3
For two parallel resistance
R= R1*R2/ R1+ R2
The characteristics of a parallel circuit are :
1. voltage is same across all parts of the circuit
2. different resistors have different current.