Derive the expression of equivalent resistance …

• Resistance of a System in Resistors:

There are two methods of joining the resistors together either in series or parallel.

Resistors in Series:

Let resistance are connected in series R_1, R₂ and R₃ then resultant resistance will be equal to the R₁+R₂+R_3.

The current flowing through each resistance is the same. The  potential  difference  across  the  ends  of  the  series  combination  is distributed  across  the resistances.

The equivalent resistance (R_s) of a series combination containing resistances R₁, R₂, R₃... is

R_s = R₁ + R₂ + R₃ +...

The equivalent resistance is greater than the greatest resistance in the combination.

Resistors in Parallel:

The  potential  difference  across  each  resistance  is  the  same  and  is  equal  to  the  potential  difference across the combination.

The main current divides itself, and different current flows through each resistance.

The equivalent resistance (R_P) of a parallel combination containing resistances R₁, R₂, R₃... is given by

1/R_P = 1/R₁ + 1/R₂ + 1/R₃ +...

The equivalent resistance is lesser than the least of all the resistances in the combination.

A series arrangement not used for connecting domestic electrical appliances in a circuit because if one electrical appliance stops working due to some defect, then all other appliance also stop working as whole circuit broken.

Different electrical appliances in a domestic circuit are connected in parallel because

1. If one electrical appliances stops working due to some defect other will not stop working.
2. In parallel connection system each appliance has own switch.
3. In parallel case each appliance gets constant voltage.