Electrical Resistance in Series

When some conductors having resistances R1,R2 and R3 etc. are joined end-on-end as in Fig. 1, they are said to be connected in series. It can be proved that the equivalent resistance or total. resistance between points A and D is equal to the sum of the three individual resistances. Being a series circuit, it should be remembered that (i) current is the same through all the three conductors (ii) but voltage drop across each is different due to its different resistance and is given by Ohm's Law and (iii) sum of the three voltage drops is equal to the voltage applied across the three conductors. There is a progressive fall in potential as we go from point A to D as shown in Fig. 2.

V = V1 + V2+ V3= IR1 + IR2 + IR3   _ _ _ _ _ _ _ _ _ Ohms Law

But  V = IR

where R is the equivalent resistance of the series combination.

IR = IR1 + IR2 + IR3 or R = R1 + R2+ R3

$\frac{1}{G}=\frac{1}{G1}+\frac{1}{G2}+\frac{1}{G3}$

As seen from above, the main characteristics of a series circuit are :

1. same current flows through all parts of the circuit.
2. different resistors have their individual voltage drops.
3. voltage drops are additive.
4. applied voltage equals the sum of different voltage drops.
5. resistances are additive.
6. powers are additive.

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