The resistance of a wire is 10ohm.The resistance of a wire whose length is twice and the radius is half,if its made of same material is..??
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R=ρl/a
Since made of same material resistivity (ρ) will be same for both
So let R1 R2 be resistance of first and second conductor l1 l2 and be their length a1 and a2 be their respective area
R1=ρ l1/a1
R2=ρ l2/a2
R1/R2 =( l1×a2)÷(l2×a1)
Considering wire to be cylinder crossectional area a=πr^2
Hence a1=πr1^2
a2=πr2^2
a1/a2 =r1^2/r2^2
Hence
R1/R2 =l1×r2^2)
Since made of same material resistivity (ρ) will be same for both
So let R1 R2 be resistance of first and second conductor l1 l2 and be their length a1 and a2 be their respective area
R1=ρ l1/a1
R2=ρ l2/a2
R1/R2 =( l1×a2)÷(l2×a1)
Considering wire to be cylinder crossectional area a=πr^2
Hence a1=πr1^2
a2=πr2^2
a1/a2 =r1^2/r2^2
Hence
R1/R2 =l1×r2^2)
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