Question

Two metallic wires A and B are connected. A has length l and radius r while B has length 2l and radius 2r. Find the ratio of effective resistance of series combination of both and resistance of wire A?

Answer 1

Wire A.

Length = l.

Radius =r.

Area =pie r2.

R1= rho x l /pie r2.

Wire B.

Length = 2l.

Radius = 2r.

Area = pie 4r2.

R2= rho x 2l/pie 4r2=rho x l /pie x 2r2.

total resistance.

1/Rp= 1/R1+1/R2.= pie r2/rho x l+2 pie r2/ rho x l.=3 pie r2/rho x l.

Rp= rho x l/ 3 pie x r2.

ratio = Rp/ R1= rho /3 pie r2divided by rho x l / pie x r2.

Rp / R1= 1 : 3.

Hope it helps you.