Question 257: AC fundamentals

Question

An inductor of $\left(\frac{100}{\pi}\right) \mathrm{mH}$, capacitor of capacitance $\left(\frac{10^{-3}}{2 \pi}\right) \mathrm{F}$ and resistance of $10 \Omega$ are connected in series with an AC voltage source of $110 \mathrm{~V}, 50 \mathrm{~Hz}$ supply. The tangent of the phase angle ' $\phi$ ' between voltage and current is

Accepted Answer

$$ \begin{aligned} & 	an \phi=\frac{X_C-X_L}{R}=\left(\frac{\frac{1}{\omega C}-\omega L}{R}ight) \ & 	an \phi=\frac{\frac{1}{(2 \pi 	imes 50) 	imes\left(\frac{10^{-3}}{2 \pi}ight)}-(2 \pi 	imes 50) 	imes\left(\frac{100}{\pi} 	imes 10^{-3}ight)}{10} \end{aligned} $$
$$ \begin{aligned} & \Rightarrow \quad 	an \phi=\frac{20-10}{10} \ & \Rightarrow \quad 	an \phi=1 \end{aligned} $$

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4

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3

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2

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1

AC fundamentals

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