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If the frequency of the ac. circuit illustrated above is ...

If the frequency of the ac. circuit illustrated above is 500/π Hz what would be the reactance in the circuit? 

(Inductance (L) = 0.9H, Capacitance (C) = 2×106

A.

0.0009Ω/π

B.

100Ω

C.

1030Ω

D.

400Ω

E.

2500Ω

Correct answer is D

Given Data: Frequency (F) = \frac{500}{π} , Inductance (L) = 0.9H, Capacitance (C) = 2 \times 10^{-6}

Total circuit reactance = Inductive reactance ( X_L ) - Capacitive reactance ( X_C )

when  ( X_L ) >  ( X_C )

Inductive reactance ( X_L ) = 2πFL = 2 \times π \times \frac{500}{π} \times 0.9 = 900Ω

Capacitive reactance ( X_C ) = \frac{1}{2πFC}\frac{1}{2 \times π \times 500/π \times 2 \times 10^{-6}}

\frac{1}{2 \times 10^{-3}} = \frac{1}{0.002}  

= 500Ω

 

Total circuit reactance =  ( X_L ) -  ( X_C ) = (900 - 500)Ω

=400Ω