Practical Exam 1 - Circuit Analysis and Design | ECE 225, Exams of Electrical Circuit Analysis

Download Practical Exam 1 - Circuit Analysis and Design | ECE 225 and more Exams Electrical Circuit Analysis in PDF only on Docsity! ECE225L PRACTICAL EXAM #1 FALL 2008 Instructions: 1. Closed-book, closed-notes, open-mind exam. 2. Work each problem on the exam booklet in the space provided. 3. Write neatly and clearly for partial credit. Cross out any material you do not want graded. Name: Problem 1: /15 Problem 2: /15 Problem 3: /15 Problem 4: /25 Problem 5: /20 Problem 6: /10 Total: /100 Periodic Waveforms: Vavg = 1 T ∫ T 0 v(t) dt, Vrms = √ 1 T ∫ T 0 v2(t) dt, FF = Vrms |V |avg , CF = Vp Vrms v(t) = Vdc + vac(t), Vavg = Vdc, Vac = √ 1 T ∫ T 0 v2ac(t), Vrms = √ V 2dc + V 2ac AC Circuits: Ṽ = Z̄Ĩ = (R + jX)Ĩ , |Ṽ | = |Z̄||Ĩ| = |Ĩ| √ R2 + X2 S̄ = P + jQ = Ṽ Ĩ∗, |S̄| = √ P 2 + Q2 = |Ṽ ||Ĩ| P = R|Ĩ|2 = |Ṽ | 2 R = |Ṽ ||Ĩ| cos(6 Ṽ − 6 Ĩ) Q = X|Ĩ|2 = |Ṽ | 2 X = |Ṽ ||Ĩ| sin(6 Ṽ − 6 Ĩ) Z̄∆ = 3Z̄Y 1 Problem 1 (15 Points) A standard color table is as follows: Color 1st Band 2nd Band 3rd Band Multiplier Tolerance Black 0 0 0 ×100 Brown 1 1 1 ×101 ±1% (F) Red 2 2 2 ×102 ±2% (G) Orange 3 3 3 ×103 Yellow 4 4 4 ×104 Green 5 5 5 ×105 ±0.5% (D) Blue 6 6 6 ×106 ±0.25% (C) Violet 7 7 7 ×107 ±0.1% (B) Grey 8 8 8 ×108 ±0.05% (A) White 9 9 9 ×109 Gold ×0.1 ±5% (J) Silver ×0.01 ±10% (K) None ±20% (M) Find the nominal value and tolerance of the following components: (a) Resistor: BLUE, GREY, RED, GOLD: (b) Precision Resistor: GREEN, BLUE, GREEN, BLACK, SILVER: (c) Capacitor: 684K 2 Problem 4 (25 Points) ~ I 1 ~ Transmission LineVoltage Source Ω Ω j125Ω−j500 Ω Ω125 Load + ~ V 2 − 20 j15 1 + − V A wattmeter W2 placed between the transmission line and the load reads W2 = 320 (W). (a) Find V2 (V). (b) Find the total reactive power Q2 (VAr) absorbed by the load. (c) Find the total apparent power S2 (VA) absorbed by the load. (d) Find the line current I1 (A). (e) Find the reading W1 (W) of a wattmeter placed between the source and the transmission line. 5 Problem 5 (20 Points) BC ~ I AB ~ I aA V(rms) V(rms) o o 120 −120 V(rms) o ~ ~ bB I −n Ω 150 150 10 10 10 150 Ω Ω Ω Ω Ω 120 120 120 0 CA ~ I cC I c C B A b ~ I a + − + − + (a) Find IL = |ĨaA| = |ĨbB| = |ĨcC | A(rms). (b) Find I∆ = |ĨAB| = |ĨBC | = |ĨCA| A(rms). (c) Find the total three-phase real power P3ph (W) delivered by the three-phase source. (d) Find the total three-phase reactive power Q3ph (VAr) delivered by the three-phase source. 6 Problem 6 (10 Points) M jX ~ 2 V − + 1 2 jXjX ** 1 ~ I ~ 1 V − + Test #1 Test #2 M jX ~ 2 V − + 2 ~ I 1 2 jXjX ** ~ 1 V − + The following tests are performed on the above linear two-winding transformer with negligible re- sistances: Test #1: With the secondary open-circuited, the primary winding is excited with a 60-Hz sinu- soidal voltage source and the following measurements are taken: V1 = 13.6 V(rms), I1 = 0.25 A(rms), and V2 = 6.2 V(rms). Test #2: With the primary open-circuited, the secondary winding is excited with a 60-Hz sinu- soidal voltage source and the following measurements are taken: V2 = 6.8 V(rms), I2 = 0.40 A. (a) Find X1, X2, and XM from these tests. (b) Find M in mH. (c) Predict the rms voltage magnitude V1 during Test #2. 7