Test 2-SP07 - Phys 208 – Theoretical Physics – Test 2...

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Unformatted text preview: Phys 208 – Theoretical Physics – Test 2 (March 2, 2007) 1. (20 pts) An AC voltage source has a voltage amplitude of 20 volts. It is connected to a resistor of 2 ohms and an inductor and capacitor as shown. The frequency of the voltage source is such that ω L = 3 ohms and ωC = 0.5 /ohm. a) Find the impedance of the circuit. b) Find the current amplitude. c) Determine the phase angle for the circuit. R L V0 C d) Write down an expression for the physical current. Does the current lead or lag the applied voltage? e) Determine the average power transferred to the circuit. ⎧1, − 1 < x < 1, 2. A function over one period is given as f ( x) = ⎨ ⎩0, − 2 < x < −1 and 1 < x < 2 a) Sketch the function over at least three periods. b) Expand it in a Fourier Series. c) To what values will the Fourier series converge to at x = 0, ± 1, ± 2 ? 3. A function is defined over one period as f ( x) =| x |, − π < x < π has a Fourier series given 2 2 by f ( x) = π 4 − cos(2nx) ∑n n2 . Use Parseval’s theorem to obtain the series π odd 2 ∞ odd n ∑n ∞ 1 4 . ⎧1, 0 < x < 1 4. a) Find the exponential Fourier transform of the function, f ( x) = ⎨ . ⎩0, otherwise b) Write f ( x) as a Fourier integral and list all the possible values of the integral. ⎧ ⎪ x, 5. Using the exponential Fourier transform the function, f ( x) = ⎨ ⎪ 0, ⎩ one finds f ( x) = ∫ 0 ∞ x <1 x >1 , sin α − α cos α iα x e dα . Use Parseval’s theorem to evaluate the integral −∞ iπα 2 2 ∞ (sin α − α cos α ) dα . 4 ∫ α ...
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This note was uploaded on 01/08/2011 for the course PHYS 208 taught by Professor J.peat during the Spring '10 term at Missouri S&T.

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