Answer to Question #162163 in Electricity and Magnetism for Naomi

Question

A resistive florescent bulb rated at 40w is designed to carry a current of 2.5A. (a) what is it's resistance? A choke is connected in series with the lamp to enable it be energiesed by the 240V,50Hz mains. (b)What is the inductance to the choke (c) A capacitor in series with a resistor is now connected in parallel to the lamp and choke so that their current lead compensates for the lag introduced by the inductor.find the value of C for this resonant circuit.

Answer 1

a)

$R=\frac{P}{I^2}=\frac{40}{2.5^2}=6.4 ~\Omega.$

b)

$U=I\omega L=2\pi \nu IL,$

$L=\frac{U}{2\pi \nu I},$

$L=\frac{240}{2\cdot 3.14 \cdot 50\cdot 2.5}\approx 306~mH.$

c)

$\nu=\frac{1}{2\pi\sqrt{LC}},$

$C=\frac{1}{4\pi^2\nu^2L},$

$C=\frac{1}{4\cdot 3.14^2\cdot 50^2\cdot 306\cdot 10^{-3}}\approx 33~\mu F.$