A 12 ~cm wire is given a shape of a right angled triangle A B C having sides 3 ~cm , 4 ~cm and 5 ~cm as shown in the figure. The resistance between two ends (AB, B C, C A) of the respective sides are measured one by one by a multi-meter. The resistance will be in the ratio:

Step-by-step solution

Resistance of side A B=R₁= 3 A Resistance of side B C=R₂= 4 A Resistance of side AC = P ₃= 5 A (Where A= Area of cross-section and = resistivity of wire) The resistance between A and B is aligned & R _ AB = R₁ (R₂+R₃ ) R₁+R₂+R₃ = 3 A ( 4 A + 5 A ) 3 A + 4 A + 5 A & = 27 12 A & Similarly R_ B C = R₂ (R₁+R₃ ) R₁+R₂+R₃ & 4 A ( 3 A + 5 A ) 3 A + 4 A + 5 A = 32 12 A & And R_ A C = R₃ (R₁+R₂ ) R₁+R₂+R₃ & = 5 A ( 3 A + 3 A ) 5 A + 3 A + 4 A = 35 12 A & R_ A B : R_ B C : R_ A C = 27 12 : 32 12 : 35 12 & =27: 32: 35 & align