Question

show that the effective resistance of a series combination is Rs=R1 +R2 +R3........... +Rn

Answer 1

in the series combination the total voltage is sum of voltages used by all resistances
so v = V1 + V2 + V3 .......vn
IR = IR1 + IR2 + IR3 .......IRn
since current is constant so
IR = I( R1+ R2+R3......Rn)
cutting I from both sides
R = R1+ R2 + .......Rn

Answer 2

In a series combination

Veff.= V1+V2+V3+...

IR eff.= IR1+IR2+IR3+...

Now as in a series combination current is constant,

Therefore,

IR eff.= I( R1+R2+R3+...)

Therefore,

R eff.= R1+R2+ R3+...