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QI-B) Given two waves characterized by yl(t) 2cos( cot -40° y2(t) 3sin( +60° y3(t) 5sin( o -10°), Find the following a) Does or lag y1(t) and by what phase angle? b) Does lag y3(t) and by what phase angle? c) Does y1(t) and by what phase angle? Q2-A) The voltage of an electromagnetic wave traveling on a transmission line is given by b (y,t) Ae ay sin(4 <106 -80x (V), where is the distance in meters from the generator (a) Find the frequency, wavelength and phase velocity of the wave (b) Aty m and ==ms,and A=20 the wave was measured to be 10V. Find a and the direction of wave propagation Q2-B) Complex numbers zl and z2 are given by Z1 -30+j40 Z2' 50260 (a) Determine the sum Z1 in polar form (b) Determine the product Z1 Z2* in rectangular form (c) Determine the ratio Z1/Z2 in polar form (d) Determine the ratio Z1*/22* in rectangular form Q3- The voltage source showni Fig below is given by expression voltage Vo(t) Let R- 49, L-4mH, L . + Vs(t) R c - Q4)A two wire line 0.505 G'=0, and 8(pF/m). (a) constant(@)= (c) phase characteristie Impedance (Zo) Q5-A)Use the appropriate expression for differential surface arca ds to determine the arca of each fthe following surfaces: a) 35r56; a/3 ;-45254 b) R=4; Q5-B) Find the volume described by, 00R<4 Q6 A)A sphere of radius 30 cm contains volume charge density 9.= sin (C/m³) Find the charge Q contained the sphere, where0 <6 9Q6-B) Given E(R,8, ©) R²cos 6 find the divergence Q7) Find the total electric field point P=(-2. 3) of the coordinates system due to the three charges, ql= 4uC and q2= 5uC. The three charges are located free space at these positions (-1. 2) and (2. 3)respectively Q8)1 Cartesian system a8 m long straight wire carrying current of 1 A in the y-direction d located aix- 20em 30em and 4sys4m.IfB 82x+93y+252 (tesla), what the magnetic force acting wire? +/ -8m . y, infinitely long, parallel wires both carrying 10A current in the same directions n 12 Point 8 c) Point C 75cm : 20cm 30cm 100cm below Find the magnitude and the direction of B point Hint use and sin(02) a)If : b) the length Radius (a)

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