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Fall04_hw3

# Fall04_hw3 - =v1 v2 is equal to 279 cos 62 20 sin 67 5 cos...

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Homework 3: due Tuesday (Sept. 21) ENEE204 (Gomez) 1. AC circuit power. The voltage on a convenient household home can be expressed as ). cos( ) ( t V t v m ϖ = a. Show that the root mean square of voltage, defined as + = T t t RMS o o dt t v T V 2 ) ( 1 (where t o is some arbitrary time origin and T is the period), is given by 2 m V . b. If the household RMS voltage is 120 volts, what is maximum value of the voltage at the outlet? 2. Practice with Complex numbers . Let j z j z j z - = + = + = 1 3 , 1 2 , 2 1 2 1 . Calculate a. ( 29 ( 29 ( 29 2 1 * 2 1 2 1 , , z z z z z z + + + b. Express z 2 ,z 3 , and z 2 +z 3 in terms of Re j θ . c. Calculate 3 2 1 z z z + , and show results in both Cartesian and Polar representation. 3. Practice with Phasors. Find the phasors that represent each of these time varying functions. a. ) 4 cos( 6 ) ( π + = t t v b. ) 3 sin( 4 ) ( + = t t i c. ) 3 sin( 4 ) 4 cos( 2 ) ( + + + = t t t v 4. More practice with Phasors. Transform the following into standard form Acos( t+ φ ). a. 4 6 ˆ j e V = b. 6 5 4 ˆ j e I = c. o j e V 39 98 . 3 ˆ - = V 5. Comparing analysis using trigonometric functions and phasors. Consider two voltages, ) 6 / cos( 20 1 - = t v and ) 3 / cos( 5 2 + = t v . a. Using trigonometric identities, show that v T

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Unformatted text preview: =v1+v2 is equal to [ ] ) 279 . cos( 62 . 20 ) sin( 67 . 5 ) cos( 82 . 19-= + = t t t v T . Hint: Expand cos’s using formula for angle addition. Note that the last b. Solve the problem using phasors. Show that 16 62 . 20 ˆ j e V-= Note that 0.279=16 o . 6. Circuits using Phasors. The impedance of a branch is given by Z=50+j40 Ω . Calculate a. Resistance b. Reactance c. Admittance d. Conductance e. Susceptance f. Magnitude of the impedance g. Phase angle of the impedance 7. Circuit Problem. A current of i(t) = 3cos(120 π t)-4sin(120 t) A is flowing through a branch with a resistor = 2 Ω , capacitor= 2F and inductor = 2H , all connected in series. Find the expression for the (steady-state) voltage across the branch in Phasor form V ˆ and time-varying form, v(t) ....
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Fall04_hw3 - =v1 v2 is equal to 279 cos 62 20 sin 67 5 cos...

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