Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 8, Problem 8.42P
Find the mutual inductance between two filaments forming circular rings of radii a and ∇a, where ∇a << a. The field should be determined by approximate methods. The rings are coplanar and concentric.
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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 8 Solutions
Engineering Electromagnetics
Ch. 8 - A point charge, Q = - 0.3 /C and m = 3 Ă— -10-16...Ch. 8 - Prob. 8.2PCh. 8 - Prob. 8.3PCh. 8 - Show that a charged particle in a uniform magnetic...Ch. 8 - Prob. 8.5PCh. 8 - Show that the differential work in moving a...Ch. 8 - A conducting strip of infinite length lies in the...Ch. 8 - Two conducting strips, having infinite length in...Ch. 8 - A current of-100az A/m flows on the conducting...Ch. 8 - A planar transmission line consists of two...
Ch. 8 - Prob. 8.11PCh. 8 - Two circular wire rings are parallel to each...Ch. 8 - An infinitely long current filament is oriented...Ch. 8 - A solenoid is 25 era long, 3 cm in diameter, and...Ch. 8 - Prob. 8.15PCh. 8 - Prob. 8.16PCh. 8 - Prob. 8.17PCh. 8 - Prob. 8.18PCh. 8 - Given a material for which ℵK = 3.1 and within...Ch. 8 - Find H in a material where (a) fir = 4.2, there...Ch. 8 - Prob. 8.21PCh. 8 - Prob. 8.22PCh. 8 - Calculate values for HO,B0, and M0 at p = c for a...Ch. 8 - Two current sheets, K0,ay, A/m at z = 0 and -K0,ay...Ch. 8 - Prob. 8.25PCh. 8 - Prob. 8.26PCh. 8 - Let đ�œ‡rj = 2 in region 1, defined by 2x + 3y —...Ch. 8 - For values of B below the knee on the...Ch. 8 - Prob. 8.29PCh. 8 - Prob. 8.30PCh. 8 - A toroid is constructed of a magnetic material...Ch. 8 - Prob. 8.32PCh. 8 - Prob. 8.33PCh. 8 - Determine the energy stored per unit length in the...Ch. 8 - Prob. 8.35PCh. 8 - Prob. 8.36PCh. 8 - A Toroid has known, reluctance R. Two windings...Ch. 8 - Prob. 8.38PCh. 8 - Conducting planes in air at Z = 0 and z = d carry...Ch. 8 - Prob. 8.40PCh. 8 - Prob. 8.41PCh. 8 - Find the mutual inductance between two filaments...Ch. 8 - Prob. 8.43PCh. 8 - Prob. 8.44PCh. 8 - Beginning with the definition, of the scalar...
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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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