Question

Show that the total effective resistance of a series combination of resistors is tje sum of individual resistance of the resistors in the combination

Answer 1

Answer:

Let's assume that we have been given n number of resistors combined in series.

We have to show that pts equivalent resistance is equal to sum of individual resistance.

Concept:

The basic thing to remember that Potential Difference is divided along the resistances in a series combination. But Current remains same along all the resistance.

$V(total) = V1 + V2 + ....n \: times$

$= > I(R \: eq.) = I(R1) + I(R2) + ....n \: times$

Cancelling I term :

$= > R \: eq. = R1 + R2 + ...n \: times$

So mathematically we can say that :

$\boxed{ \red{ \bold{ \huge{ R \: eq. = \sum \:( R )}}}}$