A wire of radius r has resistance R. If it is stretched to a radius of (3r/4) . Its resistance becomes

Question

A wire of radius r has resistance R. If it is stretched to a radius of (3r/4) . Its resistance becomes (A)  (256R/81)  (B)  (81R/256)  (C)  (16R/9)  (D)  (9R/16)

Tardigrade Admin · Accepted Answer

The resistance of a wire of length l, area of cross-section A and specific resistance p is. R=ρ (l/A) Also volume=length× area =lA=constant l1A1=l2A2 (l1/l2)=(A2/A1)=(π ( (3r/4) )/π r2)=(9/16) (R1/R2)=(l1/l2)× (A2/A1) =(9/16)× (9/16)=(81/256) R2=(256R1/81)=(256R/81)

Q. A wire of radius r has resistance R. If it is stretched to a radius of $\frac{3 r}{4}$ . Its resistance becomes

$\frac{256 R}{81}$

$\frac{81 R}{256}$

$\frac{16 R}{9}$

$\frac{9 R}{16}$

Q. A wire of radius r has resistance R. If it is stretched to a radius of 43r​ . Its resistance becomes

81256R​

25681R​

916R​

169R​

Q. A wire of radius r has resistance R. If it is stretched to a radius of $\frac{3 r}{4}$ . Its resistance becomes

$\frac{256 R}{81}$

$\frac{81 R}{256}$

$\frac{16 R}{9}$

$\frac{9 R}{16}$