A) \[~30{}^\circ ,\text{ }1\text{ }A\]
B) \[~45{}^\circ ,\text{ }0.5\text{ }A\]
C) \[~69{}^\circ ,\text{ }1.5\text{ }A\]
D) None of these
Correct Answer: B
Solution :
In an L-R circuit the phase angle is given by \[\phi ={{\tan }^{-1}}\frac{{{X}_{L}}}{R}\] where \[{{X}_{L}}\] is inductive reactance and R the resistance. Also, \[{{X}_{L}}=\omega L=2\pi \,f\,L\] Given, \[f=50\,Hz,\,\,L=0.7\,H\] \[\therefore \] \[{{X}_{L}}=2\times 3.14\times 50\times 0.7\] \[=220\,\,\Omega \] and \[R=220\,\,\Omega \] \[\therefore \] \[\phi ={{\tan }^{-1}}\frac{220}{220}=1\] \[\Rightarrow \] \[\phi ={{45}^{o}}\] Current \[I=\frac{E}{\sqrt{{{R}^{2}}+(\omega {{L}^{2}})}}\] Putting \[E=220\,V,\,\,\,\,R=220\,\,\Omega \], \[{{X}_{L}}=220\,\,\Omega \] \[\therefore \] \[I=\frac{220}{\sqrt{{{(220)}^{2}}+{{(220)}^{2}}}}=\frac{1}{\sqrt{2}}\] Watt less current is \[I\] \[\sin \phi =\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=0.5\,A\]You need to login to perform this action.
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