Question

mathematically derive an expression for resistors in series

Answer 1

If R1,R2 and R3 are three resistors connected in series across a battery of voltage V and current is I
let V1, V2 and V3 be pot. differences of these resistors respectively

then V=V1+V2+V3

using Ohms law
V=RI (1)
V1=R1×I (2)

V2=R2×I (3)

and V3=R3×I (4)

Put these values in =n (1)

RI=R1 I+R2 I+R3 I
RI=I (R1+R2+R3)

R=R1+R2+R3

Therefore in series grouping resistors are added directly.
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Answer 2

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