A) increase exponentially with constant\[4\times {{10}^{-3}}\]s
B) decrease exponentially with time constant\[1\times {{10}^{-2}}\]
C) oscillate with angular frequency\[20\,{{s}^{-1}}\]
D) first increase and then decrease
Correct Answer: B
Solution :
\[\Delta \theta =\omega \Delta t=\frac{\pi }{4}\] \[\tan \theta =\frac{X}{R}\] \[\Rightarrow \]\[X=R\] Since, current leads the voltage the circuit consists of R and C, and\[{{i}_{0}}=\frac{{{V}_{0}}}{Z}\] \[\therefore \]\[Z=\frac{{{V}_{0}}}{{{i}_{0}}}=\frac{100}{\sqrt{2}}=50\sqrt{2}\] Now, \[R\sqrt{2}=50\sqrt{2}\Rightarrow R={{X}_{C}}=50\] \[{{X}_{C}}=\frac{1}{C\omega }=50\] \[\Rightarrow \]\[C=\frac{1}{50\omega }=200\mu F\] \[\tau =RC=50\times 200\times {{10}^{-6}}=1\times {{10}^{-2}}\]sYou need to login to perform this action.
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