Question

# Two copper wire A and B of length 30m and 10m have radii 2cm and 1cm respectively. Compare the resistance of the two wires. Which will have less resistance?

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Solution

## Step 1: Given that:Length of copper wire A (lA) = 30m Radius of wire A (rA) = 2cm=2×10−2m length of copper wire B(lB) = 10m Radius of copper wire B(rB) = 1cm=10−2m Step 2: Comparison of the resistances of both wires A and B:The resistivity of a conductor is given by;R=ρlAρ=RAl Where R is the resistance of the conductor, l is the length and A is the area of the cross-section of the conductor.Since both wires, A and B are made of copper, their resistivity will be the same.ρA=ρBRAAAlA=RBABlB Putting the given values we get;RA×π×(2×10−2m)230m=RB×π×(10−2m)210m RARB=3010×4 RARB=34 Step 3: Determination of the maximum resistance between A and B:Since; RARB=34 Thus,RA=RB34RB=43RARB=1.11RAThat is;RB>RA Thus, wire B has the maximum resistance. Thus,RARB=34 And, wire B has the maximum resistance.

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