Electricity and Magnetism · Problem 8.36

MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES — Edward Purcell & David Morin

Physics — E&M · high-pass-filter

Problem

Consider the setup in Problem 8.13, but with the capacitor replaced by an inductor. Calculate the ratio

|\tilde{V}_1|^2/V_0^2

. Choose values for

R

and

L

to make

|\tilde{V}_1|^2/V_0^2 = 0.1

for a 100 Hz signal. This circuit is the most primitive of ``high-pass'' filters, providing attenuation that increases with decreasing frequency. Show that, for sufficiently low frequencies, the signal power is reduced by a factor

1/4

for every halving of the frequency.

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