ECE 2100 Section 5_Spring 2012_soln

# B using kvl and the sign conventions used determine

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• cornell2000
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Cartesian forms. b) Using KVL and the sign conventions used, determine the phasor L V ˆ in Cartesian and polar forms. (Note: Adding and subtracting is easiest in the Cartesian system.)

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3 c) Find the time function v L (t). d) Show that the three other phasor voltages add up to s V ˆ when added (tail to tip) like vectors in the complex plane. 4. The box contains a linear system with no independent sources. At the terminals a-b, v = 100cos(10 3 t +45°) V, i = 10cos(10 3 t +15°) mA. a) Write the effective value of phasors V ˆ and I ˆ . V 45 2 50 ˆ ° < = V mA 15 2 5 ˆ ° < = I b) Find the input impedance and admittance. Z = 10 4 < 30° Y = 10 -4 < -30° imag. axis real axis -10 -5 5 10 -2 5 𝑉𝑉 𝑠𝑠
4 c) Find the power consumed. ( ) ( ) mW 433 mW 30 cos 2 5 2 50 = = P d) Find the complex power and show that the real part equals P . mW 433 30 500 = < = P P 5. Answer the following questions about the circuit below if L 1 = L 2 = 2H, R = 2k , C = 0.5 µ F, and ( ) V. 45 10 cos 2 20 ) ( 3 ° + = t t v

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5 a) Determine the maximum value phasor for the input v ( t ) and the series ( L 1 + C ) and parallel (R | | L 2 ) impedances. b) Find the total impedance, the phasor for ) ( ˆ t i , and the time function i ( t ). c) Find the phasor 0 ˆ V and time function v 0 ( t ). d) Find the total power dissipated in the circuit, using at least two methods.
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• Spring '05
• KELLEY/SEYLER
• Alternating Current, Volt, Complex number, Electrical impedance, time function, value phasor voltage

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