A series circuit consists of a resistance of 15 ohms, an inductance of 0.08 henry and a condenser of capacity 30 microfarad. The applied voltage has a fequency of 500 radians. Does the current lead or lag the applied voltage and by what angle.

Solution

Given, a LCR circuit.
Resistance, R = 15 ohm
Inductance, L = 0.08 H
Capacitance, C = 30

μF

Frequency of the applied volatge = 500 radian

Here,
X_L = ωL
= 500 × 0.08
= 40 ohm

and,

\frac{1}{ωC} = \frac{1}{500 \times (30 \times 10^{- 6})}

X_{C} = 66.7 ohm

\tan ϕ = \frac{[ωL - (\frac{1}{ωC})]}{R}

= \frac{40 - 66.7}{15} = - 1.78

ϕ = - 60.65 °

Thus the current leads the applied voltage by 60.65°.

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