Match the column according to correct curve: | Wire dimension | Corresponding curve | ||
| (p) | \[\lambda =1\,\,m\] \[radius=1\,mm\] | (i) | Curve (1) |
| (q) | \[\lambda =1\,\,m\] \[radius=2\,mm\] | (ii) | Curve (2) |
| (r) | \[\lambda =\frac{1}{2}\,m\] \[radius=\frac{1}{2}\,mm\] | (iii) | Curve (3) |
A) (p)-(ii); (q)-(iii); (r)-(i)
B) (p)-(iii); (q)-(ii); (r)-(i)
C) (p)-(i); (q)-(ii); (r)-(iii)
D) (p)-(iii); (q)-(ii); (r)-(iii)
Correct Answer: D
Solution :
\[R=\frac{\rho l}{A}\,\,=\,\,\frac{\rho l}{\pi {{r}^{2}}}\] For case \[\left( p \right)\,\,R\,\,\propto \,\,\frac{(1)}{{{(1)}^{2}}}\] For case \[\left( q \right)\,\,R\,\,\propto \,\,\frac{(1)}{{{(2)}^{2}}}\] For case \[\left( r \right)\,\,R\,\,\propto \,\,\frac{(1/2)}{{{(1/2)}^{2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,so\,\,{{R}_{r}}>{{R}_{p}}>{{R}_{q}}\] \[and\,\,slope\,\,of\,\,i-v\,cure\,\,=\,\,\frac{i}{v}=\frac{1}{R}\] \[so\,\,slope\,\,r<slope\,\,p<slope\,\,q\] \[\Rightarrow \,\,\,q\,\,\to \,\,line\,(3),\,\,p\to line\,(2),\,\,r\to line\,(3)\]
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