Question

Derive mathematical relation of equivalent resistance of few resistors connected in series combination.​

Answer 1

In series combination the current flowing through the circuit is the same for all the resistors (I)but the potential Difference across each resistor is different let it be V1,V2,V3....

We know that V=IR

Total voltage across the circuit is equal to the combination of voltages across each resistor

V=V1+V2+V3.......Vn

IR=IR1+IR2+IR3.....IRn

R=Rq+R2+R3......Rn

I hope this helps ( ╹▽╹ )

Answer 2

Explanation: Equivalent resistance - The resistance of a single resistor that can replace a combination of

resistors in any given circuit without any change in potential difference across the terminals and

current through the circuit is called ‘equivalent resistance’.

∴ V = I Rs

From (2) & (3) we get, I Rs = v1 + v2 + v3

or,                                IRs = IR1 + IR2 + IR3

or,                                IRs = I (R1 + R2 + R3)

or,                                Rs = R1 + R2 + R3