A) 2 : 1
B) 1 : 2
C) 1 : 4
D) 4 : 1
Correct Answer: C
Solution :
Key Idea: Electric power dissipated is inversely proportional to resistance. The rate at which electrical energy is dissipated into other forms of energy is called electric power P. \[P=\frac{W}{t}\] but \[W=Vit\] \[\therefore \] \[P=Vi={{i}^{2}}R=\frac{{{V}^{2}}}{R}\] When heater coil is cut in two halves, then the resistance of each half becomes\[\frac{R}{2}.\] When two halves are connected in parallel, equivalent resistance is \[\frac{1}{R'}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}\] \[=\frac{1}{R/2}+\frac{1}{R/2}\] \[\frac{1}{R'}=\frac{4}{R}\] \[\therefore \] \[R'=\frac{R}{4}\] New power dissipated is \[{{P}_{2}}=\frac{{{V}^{2}}}{R'}=\frac{{{V}^{2}}}{R/4}=4{{P}_{1}}\]where \[{{P}_{1}}=\frac{{{V}^{2}}}{R}\] \[\therefore \]\[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{1}{4}\]
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