Question 366: AC fundamentals

Question

With an alternating voltage source of frequency '$f$', inductor '$L$', capacitor '$C$' and resistance '$R$' are connected in series. The voltage leads the current by $45^{\circ}$. The value of '$L$' is $\left(	an 45^{\circ}=1ight)$

Accepted Answer

$\begin{aligned}
& 	an \phi=\frac{X_L-X_C}{R} \
& \Rightarrow 	an 45^{\circ}=\left[\frac{2 \pi f L-\frac{1}{2 \pi f C}}{R}ight] \quad \ldots .\left(\because \phi=45^{\circ}ight) \
& R=\frac{(2 \pi f)^2 L C-1}{2 \pi f C} \
& 	herefore \quad L=\frac{2 \pi f \mathrm{CR}+1}{4 \pi^2 \mathrm{f}^2 \mathrm{C}}
\end{aligned}$

Answer

$\left(\frac{1+2 \pi \mathrm{fCR}}{4 \pi^2 \mathrm{f}^2 \mathrm{C}}\right)$

Answer

$\left(\frac{1-2 \pi \mathrm{fCR}}{4 \pi^2 \mathrm{f}^2 \mathrm{C}}\right)$

Answer

$\left(\frac{4 \pi^2 \mathrm{f}^2 \mathrm{C}}{1+2 \pi \mathrm{fCR}}\right)$

Answer

$\left(\frac{4 \pi^2 \mathrm{f}^2 \mathrm{C}}{1-2 \pi \mathrm{fCR}}\right)$

AC fundamentals

With an alternating voltage source of frequency 'f', inductor 'L', capacitor 'C' and resistance 'R' are connected in series. The voltage leads the current by 45^{\circ}. The value of 'L' is \left(\tan 45^{\circ}=1\right)

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