In the given circuit, inductor and capacitor are ideal. Which of the following options are CORRECT.

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Phase difference between $i_{1}$ and $i_{2}$ is $90 °$

Voltage across $R_{1}$ is 60 V and $R_{2}$ is 80 V

Current i through the source is 3A

Phase difference between voltage across inductor and voltage across capacitor is $90 °$

answer is A, B, C.

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Detailed Solution

Phasor diagram

$\begin{array}{l} \tan θ = \frac{X_{C}}{R} = \frac{40}{30} = \frac{4}{3} \\ \Rightarrow θ = 53^{0} \end{array}$

$\begin{array}{l} ∴ V_{R_{1}} = 100 \cos 53^{\circ} = 60 V \\ i_{1} = \frac{V}{Z} = \frac{100}{\sqrt{40^{2} + 30^{2}}} = \frac{100}{50} = 2 A \end{array}$

$\begin{array}{l} \tan θ = \frac{X_{L}}{R} = \frac{60}{80} = \frac{3}{4} \\ \Rightarrow θ = 37^{0} \end{array}$

$\begin{array}{l} ∴ V_{R_{2}} = 100 \cos 37^{\circ} = 80 V \\ i_{2} = \frac{V}{Z} = \frac{100}{\sqrt{60^{2} + 80^{2}}} = \frac{100}{100} = 1 A \end{array}$