First slide

Phasors and Phasor Diagrams

Question

An inductor of inductance of 1 mH, a capacitor of capacitance of $10 μF$ and a resistor resistance of $50 Ω$ are connected in series. The reactances of inductor and capacitor are same. The reactance of either of them will be

Moderate

A

$100 Ω$
B

$30 Ω$
C

$3.2 Ω$
D

$10 Ω$

Solution

Given: $ωL = \frac{1}{ωC} \Rightarrow ω^{2} = \frac{1}{LC}$
or $ω = \frac{1}{\sqrt{10^{- 3} \times 10 \times 10^{- 6}}} = \frac{1}{\sqrt{10^{- 8}}} = 10^{4}$
$X_{L} = ωL = 10^{4} \times 10^{- 3} = 10 Ω$

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