A) 0.25
B) 0.5
C) 4
D) 2
Correct Answer: C
Solution :
When electric current flows through a conductor, the conductor becomes hot. This is known as heating effect of current or Joules heating. The heat produced is given by \[Q=\frac{{{V}^{2}}t}{R\,J}cal\] When resistors are connected in parallel, resultant resistance is \[\frac{1}{{{R}_{P}}}=\frac{1}{{{R}_{1}}}+\frac{1}{{{R}_{2}}}=\frac{1}{R}+\frac{1}{R}=\frac{2}{R}\] \[\Rightarrow \] \[{{R}_{P}}=\frac{R}{2}\] Since, heat produced \[\propto \frac{1}{resistance}\] So, when resistance is calved, heat produced is doubled, hence \[{{Q}_{P}}=2\times 1000=2000\] When resistors are connected in series, \[\Rightarrow \] \[{{i}_{g}}=\frac{S}{S+G}i\] Given, \[G=6\,\Omega ,\,{{i}_{g}}=2\,A,\,i=6A\] \[\therefore \] \[2=\frac{S}{S+6}\times 6\] \[\Rightarrow \] \[2\,S+12\,=6\,S\] \[\Rightarrow \] \[4\,S=12\] \[\Rightarrow \] \[S=3\,\Omega \] Note: As the shunt resistance is small, the combined resistance of the galvanometer and the shunt is very low and hence, the ammeter has a much lower resistance than the galvanometer,
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