resistance in series and parallel

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1. Resistance in series (R_S = R₁+ R₂ + R₃)

Let R1, R2 and R3 are the three resistances that connect in series.

                                  V = V₁ + V₂ + V₃

As we know that     V = IR   So,

          IR = IR₁ + IR₂ + IR₃

          IR = I (R₁ + R₂ + R₃)

           (R_S = R₁+ R₂ + R₃)

2. Resistance in parallel (1/R_P = 1/R₁ + 1/R₂ + 1/R₃)

Let three resistances R1, R2 and R3 are connect in parallel.

I = I₁ + I₂ + I₃

As we know that      V = IR or I = V/R

So,

            V/R = V/R₁ + V/R₂ + V/R₃

            V/R = V (1/R₁ + 1/R₂ + 1/R₃)

           1/R_P = (1/R₁ + 1/R₂ + 1/R₃)

DISADVANTAGE OF SERIES CIRCUIT

1. If one electrical appliances stops working due to some defect, then all other appliances also stops working at that instant of time.
2. All the electric appliances have only one switch due to which they cannot be turned on or off separately.
3.  The appliances do not get the same voltage as that of power supply line.
4. In the series connection of the electrical appliances, overall resistances of circuit increases too much due to which current supply become low.