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- Two metallic wires A and B of the same material are connected in parallel. Wire A has length l and radius r. wire B has length 2l and radius 2r. Calculate the ratio of the equivalent resistance in parallel combination and the resistance of the wire A.

Wire A.

Length = l.

Radius =r.

Area =pie r^{2}.

R_{1}= rho x l /pie r^{2}.

Wire B.

Length = 2l.

Radius = 2r.

Area = pie 4r^{2}.

R_{2}= rho x 2l/pie 4r^{2}=rho x l /pie x 2r^{2}.

total resistance.

1/R_{p}= 1/R_{1}+1/R_{2}.= pie r^{2}/rho x l+2 pie r^{2}/ rho x l.=3 pie r^{2}/rho x l.

R_{p}= rho x l/ 3 pie x r^{2}.

ratio = R_{p}/ R_{1}= rho /3 pie r^{2}divided by rho x l / pie x r^{2}.

Rp / R_{1}= 1 : 3.

Hope it helps you++++++++