22 t 10 problem 18 the device d in the following

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Unformatted text preview: /2 f (t ) sin( nω0 t )dt = 2 Im⎡ ⎢ 0 T ⎣ ∫ T /2 ∫ 0 1 ⎡ te jnω0t e jnω0t e jnω0t ⎤ f (t )e jnω0t dt ⎤ = 2 Im ⎢ − + ⎥ = ⎥ ( jnω 0 )2 jnω 0 ⎦ 0 ⎦ ⎣ jnω 0 ⎡ e jnπ 1 ⎤ 2 ⎡1 e jnπ e jnπ 1 1 ⎤ ⎡ 2 cos nπ ⎤ = ⎢ (1 − 2 cos nπ )⎥ = −0+ 2 2 − = 2⎢− 2 Im ⎢ + + + jnπ (nπ )2 jnπ n π jnπ ⎥ π ⎣n nπ nπ ⎥ ⎦ ⎣ ⎦ ⎦ ⎣ 2⎡ sin 2πt sin 4πt 2 ⎡1 ⎤ n +1 ⎤ ⎢ n (1 + 2( −1) )⎥ f(t) = π ⎢3 sin πt − 2 + sin 3πt − 4 + ...⎥ . π ⎣ ⎦ ⎣ ⎦ 2/2 t 10 Problem 18 The device D in the following circuit is powered by a voltage v(t) = 2 + 2 cos(1000t) + cos(2000t)(V ). The current across is given by i(t) = 1 + sin(1000t) + 0.5 sin(2000t)(A) find the average power associated with D. v(t) + − D i(t) A) B) C) D) E) 2W -2W 4W -4W None of the above Problem 19 The following circuit is powered by a periodic voltage source that has the following Fourier expansion: v(t) = 21 + 20 cos(1000t) + 10 cos(2000t). Find the RMS value of the current i(t). 3Ω i(t) v(t) A) B) C) D) E) 6.68A 8.14A 7.3A 7.6A None of the above + − 4mH 11 Problem 20 For the function v(t) given below, find the value of a5 . You may use the following: t cos(αt) = cos(αt) t sin(αt) + α2 α . v(t) 2 1 0 0 1 2 3 4 5 t(s) A) 0 B) -0.0162 C) 1.27 D) -16.7 E) None of the above Good Luck 7 The following given is used in the next 5 problems. 3 electrical elements are powered by a 240VRM S , 60Hz source: I 240VRM S ∠0o + - I1 L1 I2 L2 The following is given for the three elements: L1: 240W, PF=0.6 Lag L2: 200VARS, PF=0.5 Lag L3: 100VA, PF=0 Lead Problem 11 Find the total apparent power. A) 725.67VA B) 626.33VA C) 550.2VA D) 888.8VA E) None of the above Problem 12 Find the total power factor. A) 0.567 Lag B) 0.646 Lag C) 0.808 Lag D) 0.747 Lag E) None of the above I3 L3 8 Problem 13 Find the magnitude of the total current I. A) 5.21A B) 3.02A C) 2.292A D) 7.40A E) None of the above Problem 14 Find the capacitor that needs to be placed in parallel with the loads to adjust the power factor to 0.9 Lag. A) 62.7µF B) 147µF C) 49µF D) 11.4µF E) None of the above C=2.74 mF Problem 15 Find the magnitude of I again after the power factor is adjusted as in the previous...
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