Question

what is the derivation of series combination ​

Answer 1

Answer:

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Combination of three resistors in series =>

By ohm’s law, the potential difference across R1 =V1= I R1

The potential difference across R2 = V2 = I R2.

The potential difference across R3 =V3 = I R3.

Thus, the potential difference V across this series connection of resistors

V = V1 + V2 + V3

= I R1 + I R2 + I R3

= I (R1+ R2+ R3)

Thus, in case of series connection, the equivalent resistance, Req = V/I = (R1+ R2+ R3).

For n number of resistors connected in series, the equivalent resistance Req = R1+ R2+ R3…………………Rn.

Equivalent resistance is the total resistance of the circuit. It is the single value of resistance which may replace the number of the resistors in the circuit without changing current and voltage in the network. Thus, in a series connection, the total resistance of a circuit is determined by adding the resistance of each individual resistors.

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Answer 2

Take three resistors of resistances r, r', r".

V1 = Ir

V2 = Ir'

V3 = Ir"

V = V1+V2+V3 = I(r+r'+r") ........(i)

Now, bring an effective resistance R that can replace these individual resistances r, r' and r" without changing V and I (as per definition of equivalent resistance).

V = IR .....(ii)

Now compare both the equations. You will get, R = r+r'+r"

This is the derived expression for series combination of resistors.