In the above circuit, C = 3 2 , R _ 2 = 20Ω, L = 3 10 H and R _ 1 =...

Inductive reactance ${X}_{L} = \omegaL = 100\dfrac{\sqrt{3}}{10}Ω$

$= 10\sqrt{3}Ω$

Capacitive reactance

${X}_{c} = \dfrac{1}{\omegaC} = \dfrac{1}{100 \times \dfrac{\sqrt{3}}{2} \times {10}^{- 6}}Ω = \dfrac{20000}{\sqrt{3}}Ω$

For ${i}_{1}$, phase difference between ${i}_{1}$ & voltage$tan{ϕ}_{1} = \dfrac{{x}_{L}}{R} = \dfrac{10\sqrt{3}}{10} = \sqrt{3}$

$⇒ {ϕ}_{1} = {60}^{o},$ current lagging

For ${i}_{2}$ , phase difference

$tan{ϕ}_{2} = \dfrac{{X}_{C}}{R} = \dfrac{20000}{\sqrt{3} \times 20} = \dfrac{1000}{\sqrt{3}}$

$⇒ {ϕ}_{1} \approx {90}^{o}, \text{current leading}$

$∴$ difference in phase $= {90}^{o} + {60}^{o} = {150}^{o}$