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1. Can functions V1(R,θ) = C1Rcosθ and V2 =(R,θ) = C1R2 cosθ, where C1 and C2 are arbitrary constants, be solutions of Laplace's equation in spherical coordinates? Explain.
2. A point charge Q exists at a distance d above a large grounded conducting planes.Determine-the surface charge density ρs.- the total charge induced on the conducting plane.
3. Two dielectric media with dielectric constants ε1 and ε2 are separated by a plane boundary at x = 0, A point charge Q exists in medium 1 at distance d from the boundarya - Verify that the field in medium 1 can be obtained from Q and an image charge -Q 1, both acting in medium1.b- Verify that the field in medium 2 can be obtained from Q and an image charge + Q2 coinciding with Q, both acting in medium 2.c- Determine Q1 and Q2. (Hint : Consider neighboring points P1 and P2 in media 1 and 2, respectively, and require the continuity of the tangential component of the E-field and of the normal component of the D field)
An Electric Range top burner control adjusts the duty cycle of the current and voltage supplied to surface heating element as a function of the control's dial setting. The range controller operates from a 240 VRMS single phase supply
Consider a system in which a data transfer over a bus takes 500 ns. Transfer of bus control in either direction, from processor to I/O device or vice versa, takes 250 ns. One of the I/O devices has a data transfer rate of 50 KB/s and employs DMA.
Create a state transition diagram for a simple state machine to detect a positive pulse. You choose either a Moore or Mealy machine. Write a Verilog HDL module for your state machine.
Design a low pass active filter such that its roll off attenuates frequency components a 10kHz or more by more than 30 db. This means that the magnitude of the transfer function (in db) at frequency 10kHz should be -30db or less
Binary data is transmitted at the rate of Rb bits/sec over a channel occupying a bandwidth B and the channel SNR=3 dB. If the data bit rate is increased to 2.65Rb and the bandwidth is increased to 1.75B i.
contrast the electron and hole drift velocities through a 10-µm layer of intrinsic silicon across which a voltage of 5 V is imposed. Let µn = 1350 cm²/V·s and µp = 480 cm²/V·s.
A 100 kVA 2000/400 V, 50 Hz single-phase transformer gave the following test results. With 2000 V applied to the primary with the secondary on open circuit: current 2 A, power 1400 W With the secondary short-circuited and 112 V applied to the primary..
Pure ethylene (C2H4) and oxygen are fed to a process for the manufacture of ethylene oxide (C2H4O) C2H4 + ½ O2? C2H4O The process flow diagram is shown below. The catalytic reactor operates at 300 °C and 1.2 atm. Under these conditions
A 5mm-long 100W microstrip line with velocity factor of 0.4 is used to fabricate a resonator at 3GHz. It is connected to an inductor at one end. Determine whether the other end of the microstrip line should be short circuited
A digital system has a clock generator that produces pulses at a frequency of 16 MHz. Design a circuit (draw the logic diagram) that provides a clock with a cycle time of 250 ns.
Design a logic circuit, LOGARITHM that converts an input number X to its logarithm, log(X). Input X is given as an unsigned real number such that, 1.00
Consider a multimode silica fiber that has a core refractive index of n1 = 1.48 and cladding index n2 = 1.46. Find the critical angle, numerical aperture and the acceptance angle.
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