Resistors in Series

R1, R2, and R3 are three resistance-connected end-to-end across a voltage source, V. VI. V2 and V3 are voltage drops in RI, R2, and R3 respectively I is the total current. From the figure, 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 a series combination of resistors, the total resistance is equal to the sum of all individual resistance.

Resistors in series Characteristics

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

   I_T=I₁-I₂-I₃

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

   R_T = R₁ + R₂ + R₃ ………………. R_N

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

   V_T= V₁+V₂+V₃IR_T = IR₁ + IR₂ + 1R₃

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

   P_T=P₁+P₂+P₃

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