# Applied mathematics for radio and communication engineers - download pdf or read online By Carl E. Smith

Arithmetic, consultant, How-to, Communications, Engineering

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Download PDF by Carl E. Smith: Applied mathematics for radio and communication engineers

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Extra resources for Applied mathematics for radio and communication engineers

Example text

Proceeding as before, using Eq. 5) = -10 = 20( - VR; R; Note: The square of a negative number is a positive number. 22 Ans. The angle of the resultant vector R by Eq. (12) is R. 485 Note: This is negative because it is in the second quadrant instead of the first. From trigonometric tables, 'Y = 82°56' This, however, is the angle vector R makes with the negative x-axis. If we subtract this from 180° we get the angle" vector R makes with the positive It will be noted that this equation is like Eq.

__ + X2 R2]2 1 2 -­ X2 + R2 Squaring both sides (Rule 7) and turning the equation around, R2 yE2 - = Transposing J2 R2, Dividing by (X2 Dividing by I, y- I Squaring both sides to remove the radical, E Factoring 1 2 , 1=-­ yR2 + X2 E - yE2 - R2I2 Clearing of fractions, Solving for R was slightly more complicated but each step in itself was quite simple. The student should write out each step when solving problems until the procedure is thoroughly under­ stood. If the steps are written out in detail, mistakes will be less likely to occur.

This chflcks the value given above. = 60 10 = - ylO,OOO - 6,400 10 = 6 ohms reactance 52 ALGEBRA APPLIED MATHEMATICS In case the student may not know when to square or when to extract a square root, it may be helpful to remember that X = (VX)2, so if X2 is given, extract the square root to get X and if VX is given, square the quantity to get X. Of COurse rules 7 and 8 must be remembered when performing these operations on equations. Both sides of the equation must be treated alike. In the equation, XI = Xc we know that XI = 27rfL and 1 Xc = 27rfC Therefore, by substituting as pointed out in rule 10, we can write 27rfL = 1 27rfC Exercises 1.