The ripple voltage across a capacitor has period and

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier series and periodic decomposition

Problem

The ripple voltage across a capacitor has period LL and, within one period −L/2<x≤L/2-L/2 < x \le L/2, rises linearly: v(x)=V02xL,V0=9.00 mV,v(x) = V_0\frac{2x}{L}, \qquad V_0 = 9.00\,\mathrm{mV}, with a jump back to −V0-V_0 at the end of each period. This is the sawtooth shape, with amplitude parameter A=V0A = V_0 in the sawtooth coefficient formula bn=(−1)n+12Anπb_n = (-1)^{n+1}\dfrac{2A}{n\pi}. ((a)) Find b1b_1. ((b)) Find b2b_2. ((c)) Find b3b_3.

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