Series and parallel connection of resistors

 TYPES OF CONNECTIONS:

Electric components can be connected in two ways

SERIES:

 When negative terminal of first component is connected to positive terminal of second component, negative terminal of second component is connected to positive terminal of third component and so on, then the components are said to be connected in series.

PARALLEL:

 when the positive terminals of all the components are connected to one end and the negative terminals of all the components are connected to another end, then the components are said to be connected in parallel.

HOW TO FIND EQUIVALENT RESISTANCE OF COMBINATION OF RESISTORS CONNECTED IN SERIES AND PARALLEL?

RESISTORS CONNECTED IN SERIES:

In series connection of resistors there is only one path for the flow of current in the circuit. Hence, the current in the circuit is equal to i. But potential difference varies depending upon the resistance of a resistor.

According to Ohm’s law,

Potential difference across R1 is , V1 = iR1

Potential difference across R2 is , V2 = iR2

Potential difference across R3 is , V3 = iR3

Let Req is the equivalent resistance of the combination of resistors in series.

So, we have V = i Req  (ohm’s law)

Substituting the values of V1, V2, V3 and V in the  above equation, we get

iReq = iR1 + iR2 + iR3

Req = R1 + R2 + R3

From the above equation you can conclude that the sum of individual resistances is equal to their equivalent resistance when the resistors are connected in series. This is advantage of series combination. But we have one disadvantage too. If circuit breaks at any point, no device will work in series because current will not flow through the circuit.

PARALLEL COMBINATION OF RESISTORS:

In parallel combination the potential difference at two extreme ends will be constant. But current splits at each junction.

According to the Ohm’s law,

Current through R1 is, i1 = V/R1

Current through R2 is, i2 = V/R2

Current through R3, is, i3 = V/R3

Let Req be the equivalent resistance of the

resistors is parallel. 

Then we get; i = V/Req

Substituting the values I, I1, I2 and I3 in above equation, we get

V/Req = V/R1 +V/R2 + V/R3

1/Req = 1/R1 + 1/R2 + 1/R3

Let two resistors R1 and R2 are connected in parallel,

1/Req = 1/R1 + 1/R2

“The equivalent resistance of a parallel combination is less than the resistance of each of the resistors”

  

  The main drawback of parallel combination is, the output of the combination will be less. And the main advantage of parallel combination is if circuit breaks at a point, only the device connected to that point will not work but remaining all devices will work.