Question

25. Tow wires, when connected in series, have an equivalent resistance of 18 ohm and
when connected in parallel an equivalent resistance of 4 Ω. Find their resistances.
Α. 10 Ω, 33 Ω
D. 19 Ω, 2 Ω
Β. 12 Ω, 6 Ω
Ε. 35 Ω, 3 Ω
C. 26 Ω, 2 Ω

Answer 1

let the Resistance be R¹ and R²

in series= R¹ + R² =18...........1

in parallel = 1/R¹+ 1/R² = 4

= R¹+R²/R¹R² = 4

put R¹ + R² =18 in R¹+R²/R¹R² = 4

18 /R¹R² = 4

R¹R² = 18/4 =9/2

(a+b)²-(a-b)² = 4ab formula

(R¹+R²)²- (R¹-R²)² = 4R¹R²

18²- (R¹-R²)² = 4×9/2 = 18

(R¹-R²)² = 324-18= 306

(R¹-R²) = √306 = 17.49...........2

form eq1 and eq2

2R¹ = 35.49

R¹ = 35.49/2 = 17.745

put R¹ = 17.745 in any eq

17.745 +R² = 18

R² = 0.25