Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
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Chapter 3, Problem 3.2P
To determine
The area of the parallelogram from the cross product of the
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-E1 + VR1 + VR4 – E2 + VR3 = 0 -------> Loop 1 (a)
R1(I1) + R4(I1 – I2) + R3(I1) = E1 + E2 ------> Loop 1 (b)
R1(I1) + R4(I1) - R4(I2) + R3(I1) = E1 + E2 ------> Loop 1 (c)
(R1 + R3 + R4) (I1) - R4(I2) = E1 + E2 ------> Loop 1 (d)
Now that we have loop 1 equation will procced on finding the equation of I2 current loop. However, a reminder that because we are going in a clockwise direction, it goes against the direction of the current. As such we will get an equation for the matrix that will be:
E2 – VR4 – VR2 + E3 = 0 ------> Loop 2 (a)
-R4(I2 – I1) -R2(I2) = -E2 – E3 ------> Loop 2 (b)
-R4(I2) + R4(I1) - R2(I2) = -E2 – E3 -----> Loop 2 (c)
R4(I1) – (R4 + R2)(I2) = -E2 – E3 -----> Loop 2 (d)
These two equations will be implemented to the matrix formula I = inv(A) * b
R11 R12
(R1 + R3 + R4)
-R4
-R4
R4 + R2
10.2 For each of the following groups of sources, determineif the three sources constitute a balanced source, and if it is,determine if it has a positive or negative phase sequence.(a) va(t) = 169.7cos(377t +15◦) Vvb(t) = 169.7cos(377t −105◦) Vvc(t) = 169.7sin(377t −135◦) V(b) va(t) = 311cos(wt −12◦) Vvb(t) = 311cos(wt +108◦) Vvc(t) = 311cos(wt +228◦) V(c) V1 = 140 −140◦ VV2 = 114 −20◦ VV3 = 124 100◦ V
Apply single-phase equivalency to determine the linecurrents in the Y-D network shown in Fig. P10.13. The loadimpedances are Zab = Zbc = Zca = (25+ j5) W
Chapter 3 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 3 - Find AB for the following: A=2ax3ay+4az,B=5ay1az...Ch. 3 - Prob. 3.2PCh. 3 - Given the vertices of a triangle...Ch. 3 - A segment of conductor on the z–axis extends...Ch. 3 - Prob. 3.5PCh. 3 - Prob. 3.6PCh. 3 - A square conductive loop in the shape 10.0 cm is...Ch. 3 - A conductive loop in the x–y plane is bounded by...Ch. 3 - How close do you have to be to the middle of a...Ch. 3 - For the ring of current described in MATLAB 3.2,...
Ch. 3 - A solenoid has 200 turns, is 10.0 cm long, and has...Ch. 3 - For the solenoid of the previous problem, plot the...Ch. 3 - Prob. 3.13PCh. 3 - Two infinite extent current sheets exist at z=2.0m...Ch. 3 - An infinite extent current sheet with K=6.0ayA/m...Ch. 3 - Given the field H=3y2ax, find the current passing...Ch. 3 - Given a 3.0–mm–radius solid wire centered on...Ch. 3 - Given a 2.0–cm–radius solid wire centered on...Ch. 3 - An infinitesimally thin metallic cylindrical shell...Ch. 3 - A cylindrical pipe with a 1.0–cm wall thickness...Ch. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - Consider the toroid in Figure 3.55 that is tightly...Ch. 3 - Find A for the following fields: A=3xy2/zax...Ch. 3 - Find J at (3m,60,4m) for H=(z/sin)a(2/cos)azA/mCh. 3 - Suppose H=y2ax+x2ayA/m .(a) Calculate HdL around...Ch. 3 - Prob. 3.27PCh. 3 - Suppose you have the field H=rcosaA/m. Now...Ch. 3 - Prob. 3.29PCh. 3 - Suppose an infinite extent sheet of current with...Ch. 3 - Prob. 3.31PCh. 3 - A 1.0nC charge with velocity 100.m/s in the y...Ch. 3 - A 1.0nC charge with velocity 100.m/s in the z...Ch. 3 - A 10.nC charged particle has a velocity...Ch. 3 - What electric field is required so that the...Ch. 3 - An electron (with rest mass Me=9.111031kg and...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Suppose you have a pair of parallel lines each...Ch. 3 - In Figure 3.57, a 2.0-A line of current is shown...Ch. 3 - Modify MATLAB 3.4 to find the differential force...Ch. 3 - Prob. 3.43PCh. 3 - A square loop of 1.0-A current of side 4.0 cm is...Ch. 3 - A current sheet K=100axA/m exists at z=2.0cm. A...Ch. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - A solid nickel wire of diameter 2.0 mm evenly...Ch. 3 - Prob. 3.49PCh. 3 - The plane y = O separates two magnetic media....Ch. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - Prob. 3.54PCh. 3 - Prob. 3.55PCh. 3 - Prob. 3.56PCh. 3 - Prob. 3.57PCh. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - In Figure 3.59, a 2.0-cm-diameter toroidal core...Ch. 3 - Suppose the 2.0-cm-diameter core of the toroid in...Ch. 3 - Prob. 3.64PCh. 3 - Consider a 1.0-mm air gap in Figure 3.49a. The...
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- 10.8 In the network of Fig. P10.8, Za = Zb = Zc = (25+ j5) W.Determine the line currents.arrow_forwardUsing D flip-flops, design a synchronous counter. The counter counts in the sequence 1,3,5,7, 1,7,5,3,1,3,5,7,.... when its enable input x is equal to 1; otherwise, the counter count 0. Present state Next state x=0 Next state x=1 Output SO 52 S1 1 S1 54 53 3 52 53 S2 56 51 0 $5 5 54 S4 53 0 55 58 57 7 56 56 55 0 57 S10 59 1 58 58 S7 0 59 S12 S11 7 $10 $10 59 0 $11 $14 $13 5 $12 S12 $11 0 513 $15 SO 3 S14 $14 S13 0 $15 515 SO 0 Explain how to get the table step by step with drawing the state diagram and finding the Karnaugh map.arrow_forwardFor the oscillator resonance circuit shown in Fig. (5), derive the oscillation frequency Feedback and open-loop gains. L₁ 5 mH (a) ell +10 V R₁ ww R3 S C2 HH 1 με 1000 pF 100 pF R₂ 1 με RA H (b) +9 V R4 CA 470 pF C₁ R3 HH 1 με R₁ ww L₁ 000 1.5 mH R₂ ww Hi 1 μF L2 m 10 mHarrow_forward
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