Question 425: AC fundamentals

Question

An inductive coil has a resistance of $$100 ~\Omega$$. When an a.c. signal of frequency $$1000 \mathrm{~Hz}$$ is applied to the coil the voltage leads the current by $$45^{\circ}$$. The inductance of the coil is $$\left(	an 45^{\circ}=1ight.$$)

Accepted Answer

$$\begin{aligned} 	an \phi & =	an 45^{\circ}=\frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}} \ 	herefore \frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}} & =1 	ext { or } \mathrm{X}_{\mathrm{L}}=\mathrm{R} \ 	herefore 2 \pi \mathrm{fL} & =\mathrm{R} \ & 	ext { or } \mathrm{L}=\frac{\mathrm{R}}{2 \pi \mathrm{f}}=\frac{100}{2 \pi 	imes 1000}=\frac{0.05}{\pi} \mathrm{H}\end{aligned}$$

Answer

$$\frac{0.25}{2 \pi} \mathrm{H}$$

Answer

$$\frac{0.05}{\pi} \mathrm{H}$$

Answer

$$\frac{0.25}{\pi} \mathrm{H}$$

Answer

$$\frac{0.5}{\pi} \mathrm{H}$$

AC fundamentals

An inductive coil has a resistance of $100 ~\Omega. When an a.c. signal of frequency 1000 \mathrm{~Hz} is applied to the coil the voltage leads the current by 45^{\circ}. The inductance of the coil is \left(\tan 45^{\circ}=1\right.$)

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