SERIES ELEMENTS AND VOLTAGE DIVISION
Two or more elements are in series if they are cascaded or connected sequentially and
consequently carry the same current. The equivalent resistances of any number of resistors connected in series is the sum of the individual resistances.
Vs = V1 + V2 + V3
Vs= IR1 + IR2 + IR3
= I(R1 + R2 + R3)
= I Req
Req = R1 + R2 + R3
Three resistances R1,R2,R3 are connected in series. The current passing through all the
elements connected in series is same, I. In the above figure1, according to KVL, sum of voltage drops in a closed loop is zero.
Therefore voltage applied divides across the series connected elements.
Applications of Series Circuits :
1. Decorative serial sets, number of bulbs with low voltage ratings connected in series
across existing rated voltage.
2. Voltage distribution or tapping.
PARALLEL ELEMENTS AND CURRENT DIVISION
Two or more elements are in parallel if they are connected to the same two nodes and
consequently have the same voltage across them. The parallel connected elements have the same voltage across them.
V= i1 R1 = i2 R2 ...(1)
At Node A ( I = i1 + i2 )...(2)
From (1) and (2)
V/Req = V/R1 + V/R2
1/Req = 1/R1 +1/R2
Req = R1. R2 / (R1+R2)
The equivalent resistance of the parallel resistors is equal to the product of their resistances divided by their sum.
The equivalent conductance connected in parallel is the sum of their individual conductance.
STAR – DELTA TRANSFORMATION
Star connection and delta connection are the two different methods of connecting three basic
elements which cannot be further simplified into series or parallel.