A) 4>3>1>2
B) 4>2>1>3
C) 1>2>3>4
D) 3>1>2>4
Correct Answer: D
Solution :
(d) 3>1>2>4 Resistance of a wire, \[R=\frac{\rho l}{A}\] Rate of energy dissipated as heat is \[H=\frac{{{V}^{2}}}{R}=\frac{{{V}^{2}}A}{\rho l}\] For wire 1, \[{{H}_{1}}=\frac{{{V}^{2}}A}{\rho L}\] For wire \[2,\,{{H}_{2}}=\frac{{{V}^{2}}A}{(1.2\rho )(1.2L)}=\frac{0.694{{V}^{2}}A}{\rho L}=0.694{{H}_{1}}\] For wire 3, \[{{H}_{3}}=\frac{{{V}^{2}}A}{(0.9\rho )(0.9L)}=\frac{1.23{{V}^{2}}A}{\rho L}=1.23{{H}_{1}}\] For wire 4, \[{{H}_{4}}=\frac{{{V}^{2}}A}{(\rho )(1.5L)}=\frac{0.666{{V}^{2}}A}{\rho L}=0.666{{H}_{1}}\] \[\therefore {{H}_{3}}>{{H}_{1}}>{{H}_{2}}>{{H}_{4}}\]
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