derive an expression for the resistance of two conductors connected in;

(a) in series
(b) in parallel

1 answer

(a) In series: When two conductors are connected in series, the total resistance is the sum of the individual resistances. Therefore, the expression for the total resistance (R_total) in series can be written as:

R_total = R1 + R2

where R1 and R2 are the resistances of the individual conductors.

(b) In parallel: When two conductors are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. Therefore, the expression for the total resistance (R_total) in parallel can be written as:

1/R_total = 1/R1 + 1/R2

Solving for R_total, we get:

R_total = (R1 * R2) / (R1 + R2)

where R1 and R2 are the resistances of the individual conductors.