Resistors in Series

R1, R2 and R3 are three resistance-connected end to end across voltage source, V. VI. V2 and V3 are voltage drops in RI, R2 and R3 respectively I is the total current. From the fig we see that

V_T= V_I+V₂+V₃ ---> (1)

We know that

Vs=IR—> (2)

Put eq (2) in eq (1) we get

IR_T= IR₁+IR₂+IR₃--------> (3)

IR_T = I(R₁+R₂+R₃) —>(4)

Divide both sides by I we get

R_T = R₁+R₂+R₃

In general

R_T = R₁+R₂+R₃........................... R_n

Where n=1,2,3,4,........

CONCLUSION

In series combination of resistance the total resistance is equal to the sum of all individual resistance.

Resistance in series Characteristics

1. In series circuit the current flows in each resistor is same.

   I_T=I₁-I₂-I₃

2. In series circuit the total resistance is equal to the sum of all circuit resistance.

   R_T = R₁ + R₂ + R₃ ................... R_N

3. In series circuit when the value of one resistor is increased as a result the total circuit resistance is increases.
4. In series circuit there is the different voltage drop across each resister, which depends on the value of resister.
5. In series circuit the total voltage is equal to the sum of voltage drop across each resister.

   V_T= V₁+V₂+V₃

   IR_T = IR₁ + IR₂ + 1R₃

6. In series if there is fault in the one resister as a result the complete circuit will not work.
7. In series circuit the total power is equal to the sum of all power, which are across the each resister.

   P_T=P₁+P₂+P₃

As there are single path in this circuit so they are not used commonly.