First slide

Phasors and Phasor Diagrams

Question

For a series RLC circuit, $R = X_{L} = 2 X_{C} .$ The impedance of the circuit and phase difference between V and i will be

NA

Solution

$X_{L} = R, X_{C} = R / 2$
$∴ tanϕ = \frac{X_{L} - X_{C}}{R} = \frac{R - \frac{R}{2}}{R} = \frac{1}{2}$
$\Rightarrow ϕ = \tan^{- 1} (1 / 2)$
Also, $Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = \sqrt{R^{2} + \frac{R^{2}}{4}} = \frac{\sqrt{5}}{2} R$

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