Question

The equivalent resistances of two wires connected in series and in parallel are 25 ohm and 4 ohm respectively. Calculate the resistance of each wire.

Answer 1

5ohms and 20ohms

Step-by-step explanation:

Let the resistance of each wire be R1 and R2, if the equivalent resistance in series is 25 ohms, then;

R1 + R2 = 25 ...1

If the equivalent in parallel is 4 ohm, then;

1/R1 + 1/R2 = 1/4

R2+R1/R1R2 = 1/4

Cross multiply

4(R2+R1) = R1R2 ...2

From 1;

R1 = 25 - R2 ... 3

Substitute 3 into 2

4(R2+25-R2) = (25-R2)R2

4(25) = (25-R2)R2

100 = 25R2 - R2²

R₂² -25R₂+100 = 0

R₂² -20R₂-5R₂+100 = 0

R₂(R₂-20)-5(R₂-20) = 0

(R₂-5)(R₂-20)=0

R₂ = 5 or 20

Since R₁ = 25-R₂

R₁ = 25 - 5

R₁ = 20

Hence the resistances are 5ohms and 20ohms