Fundamentals of Electromagnetics with Engineering Applications
1st Edition
ISBN: 9780470105757
Author: Stuart M. Wentworth
Publisher: Wiley, John & Sons, Incorporated
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Chapter 4, Problem 4.42P
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4 Using phasor techniques, solve for the current in
the circuit shown in Figure P4.54.
3H
ww
v:(t) = 12 cos 3t V
1/3 F
9 Inthe circuit of Figure P4.49,
i,(1) = 1, cos (wt +E
I, = 13 mA
C = 0.5 µF
w = 1,000 rad/s
a. State, using phasor notation, the source current.
b. Determine the impedance of the capacitor.
c. Using phasor notation only and showing all work,
determine the voltage across the capacitor,
including its polarity.
You can solve the problem using Euler's formula to go from a polar (phasor) representation to a rectangular (real + imaginary) representation and then back to a polar (phasor) representation. The result is a rather complicated expression.....that doesn't mean it is wrong!
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Chapter 4 Solutions
Fundamentals of Electromagnetics with Engineering Applications
Ch. 4 - How long does it take for charge density to drop...Ch. 4 - At a particular point in a slab of silver, a...Ch. 4 - A current density is given by J=e.01taA/m2. Find...Ch. 4 - At t=0s, 60.0C is evenly distributed throughout a...Ch. 4 - A propagating electric field is given by...Ch. 4 - A 10.0-MHz magnetic field travels in a fluid for...Ch. 4 - Modify the simple wave program in MATLAB 4.1 to...Ch. 4 - Modify the traveling wave program in MATLAB 4.2 to...Ch. 4 - Prob. 4.9PCh. 4 - A bar magnet is dropped through a conductive ring....
Ch. 4 - Considering Figure 4.7, suppose the area of a...Ch. 4 - Sometimes a transformer is used as an impedance...Ch. 4 - Prob. 4.13PCh. 4 - The mean length around a nickel core of a...Ch. 4 - A triangular wire loop has its vertices at the...Ch. 4 - Referring to Figure 4.23, suppose a conductive bar...Ch. 4 - Suppose we have a conductive bar moving along a...Ch. 4 - The radius r of a perfectly conducting metal loop...Ch. 4 - Rederive Vemf for the rectangular loop of Figure...Ch. 4 - In Figure 4.16, replace the rectangular loop with...Ch. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - A Faraday disk generator is similar to the...Ch. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Suppose a vector field is given by A=2cosaz Verify...Ch. 4 - A pair of 60cm2 area plates are separated by a...Ch. 4 - Plot the loss tangent of seawater ( =4S/m and r=81...Ch. 4 - A 1.0-m-long coaxial cable of inner conductor...Ch. 4 - Suppose in free space that E(z,t)=5.0e2ztaxV/m. Is...Ch. 4 - An electric field propagating in a lossless...Ch. 4 - A magnetic field propagating in free space is...Ch. 4 - Find the instantaneous expression for E for the...Ch. 4 - Given, at some point distant from a source at the...Ch. 4 - In a lossless, nonmagnetic media, the magnetic...Ch. 4 - Suppose, in a nonmagnetic medium of relative...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Find E(z,t) in Problem 4.32 using phasors.Ch. 4 - Prob. 4.41PCh. 4 - Find H(y,t) in Problem 4.36 using phasors.Ch. 4 - In MATLAB 4.4, a polar plot of the phasor...
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- Could you solve the following as it is written and then do so again with a different given capacitance and an unknown load, please?arrow_forwardCan you please explain how do I write ZL from rectangular form to a phasor form (see attached the result highlighted in green)? My book says the result should be 3.142<90 Ohms which in phasor form. I don't know how this gets convertedarrow_forwardQUESTION 8 Consider the complex number show below. Z4 = 42 – 90° Convert Z4 to rectangular form and specify its real part in the box below.arrow_forward
- In your own terms, explain what is a phasor and show the relationshipbetween polar and rectangular forms of phasors.arrow_forwardWhen applying cosine as the base function for phasors, what part is used in Euler's identity?arrow_forwardThe voltage across an inductor plotted as a functionof time is shown in Figure P4.14. If L = 0.75 mH,determine the current through the inductor att = 15 μs.arrow_forward
- 4- Write two examples about converting an equation from rectangular form [contain x,y] to polar equation form, [contain r,0]. 5- Write two examples about symmetry tests in polar graphsarrow_forwardFor the circuit shown in Figure (4.a): i) Find the voltage across the capacitor in polar form. ii) Draw the phasor diagram relationship of Vc and Vs. ii) Is this circuit pre-dominantly inductive or capacitive? Why? R1=1ko X, = 5000 Vs= 50 |0 Xe = 5000 R2=1ko Figure 4.aarrow_forwardFor the circuit shown in Figure (4.a): i) a) Find the voltage across the capacitor in polar form. ii) Draw the phasor diagram relationship of Vc and Vs. iii) Is this circuit pre-dominantly inductive or capacitive? Why? R1=1kN X1 = 5000 Vs= 50 0 Xe = 5000 R2=1knarrow_forward
- 4.55 Use phasor techniques to solve for the voltage v(t) shown in Figure P4.55. 10 cos 2t A 3 23 3 H 1/3 F v(1) ellarrow_forwardThe plot of a time-dependent voltage is shown inFigure P4.12. The waveform is piecewise continuous.If this is the voltage across an inductor L = 35 mH,determine the current through the inductor. Assume theinitial current is iL(0) = 0.arrow_forward5 Using phasor techniques, solve for the voltage v in the circuit shown in Figure P4.55. i(t) = 10 cos 2t A 303 3 Hg 1/3 F v(t)arrow_forward
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