A resistor ‘R’ of resistance $2000 Ω$ and two similar capacitor ‘A’ and ‘B’ of capacitance $1 μF$ each are connected with an A.C. source of 200 volt and 500 rad/s. Now switch is closed at t=0, choose the correct option(s).

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The phase difference between applied voltage and voltage across the capacitor A is $\tan^{- 1} (\frac{1}{3})$

Power dissipated through resistor is 4 watt.

The phase difference between current supplied by source and current in the capacitor ‘B’ is zero.

The current in the capacitor ‘A’ is $\frac{1}{5 \sqrt{20}}$ ampere.

answer is A, C, D.

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Detailed Solution

$x_{c} = \frac{1}{ωC} = 2000 Ω . . . (i)$

$i^{2} = {(i_{C})}_{A}^{2} + {(i_{R})}^{2}; z' = 1000 \sqrt{2} . . . (ii)$

$V^{2} = {(V_{C})}_{B}^{2} + {(V')}^{2} + 2 V_{C} . V' \cos 45 °; z = \sqrt{20} . {(10)}^{3}; i = \frac{200}{\sqrt{20} \times 10^{3}} = \frac{1}{5 \sqrt{20}} . . . (iii)$

$i_{R} = icos 45 ° {(i_{C})}_{A} = icos 45 ° tanα = \frac{V' \sin 45 °}{{(V_{C})}_{B} + V' \cos 45 °} = \frac{1}{3} . . . (iv) Power = i^{2} R = {(\frac{1}{5 \sqrt{20}})}^{2} . 2000 = 4 W$