Question 23.20: Find the average power developed across a 1 Ω resistor by a ......
Find the average power developed across a 1 Ω resistor by a voltage signal with period 2π given by
v(t)=\cos t-\frac{1}{3} \sin 2 t+\frac{1}{2} \cos 3 tStep-by-Step
We note that v{t) is periodic with period T = 2π: v(t) is already expressed as a Fourier series with a_1=1, a_3=\frac{1}{2} \text { and } b_2=-\frac{1}{3}. All other Fourier coefficients are 0. The instantaneous power is (v(t))^2 and hence the average power over one period is given by
P_{\mathrm{av}}=\frac{1}{2 \pi} \int_0^{2 \pi}(v(t))^2 \mathrm{~d} tTherefore, using Parseval’s theorem we find
P_{\mathrm{av}}=\frac{1}{2}\left(1^2+\left(-\frac{1}{3}\right)^2+\left(\frac{1}{2}\right)^2\right)=0.68 \mathrm{~W}Related Answered Questions
Question: 23.22
Verified Answer:
For the capacitor,
v_{\mathrm{o}}=\frac{i}{...
Question: 23.21
Verified Answer:
We find
\begin{aligned} c_n & =\frac{1}...
Question: 23.19
Verified Answer:
The function illustrated in Figure 23.24 is given ...
Question: 23.18
Verified Answer:
This function is defined by f(t)=t,-\pi<...
Question: 23.17
Verified Answer:
As usual we sketch the function first (Figure 23.1...
Question: 23.16
Verified Answer:
Assume that f (t) can be expressed in the form
[la...
Question: 23.15
Verified Answer:
As usual we sketch f (t), as shown in Figure 23.16...
Question: 23.14
Verified Answer:
As usual we sketch f (t) first as this often provi...
Question: 23.13
Verified Answer:
The function f (t) is shown in Figure 23.14. Note ...
Question: 23.12
Verified Answer:
We must evaluate
\int_{-\pi / \omega}^{\pi ...