SOLUTION: The impedance of a parallel conductor (symbol Z) is given by the formula: Z = 276log(2D/d) where D is the separation of the 2 metallic plates in the conductor and d is the di

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The impedance of a parallel conductor (symbol Z) is given by the formula: Z = 276log(2D/d) where D is the separation of the 2 metallic plates in the conductor and d is the di      Log On


   

Question 635644: The impedance of a parallel conductor (symbol Z) is given by the formula:
Z = 276log(2D/d)
where D is the separation of the 2 metallic plates in the conductor and d is the diameter of the conductors.
a) calculate the impedance when the separation of the plates is 0.5mm and the diameter is 4mm. - (i just substitute the numbers in right?)
b) make D the subject of the formula
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
a) Yes, just substitute the numbers and simplify (using your calculator at least to find the log)

b) "make D the subject..." is an unusual way of saying "Solve for D"
Z+=+276log%28%282D%2Fd%29%29+
To solve for D we need to "peel away" the rest of the right side of the equation. First, we can get rid of the 276 by dividing both sides by it:
Z%2F276+=+log%28%282D%2Fd%29%29+
To eliminate the log, we rewrite the equation in exponential form. In general log%28a%2C+%28p%29%29+=+q is equivalent to: p+=+a%5Eq. Using this pattern (and the fact that the base of "log" is 10) on our equation we get:
10%5E%28%28Z%2F276%29%29+=+2D%2Fd
Now we can eliminate the d by multiplying both sides by it:
d%2A10%5E%28%28Z%2F276%29%29+=+2D
And the 2 goes away if we divide by it:
%28d%2A10%5E%28%28Z%2F276%29%29%2F2%29+=+D... or multiply by 1/2:
%281%2F2%29%2Ad%2A10%5E%28%28Z%2F276%29%29+=+D