Converting a formula based on common logarithms
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Question 1: The capacitance between two parallel wires in space is given by the formula
C = 1 / {3.6 ln [(d-r)/r]
where d is the spacing between wire centers in centimeters, r is the wire radius in centimeters, and C is in picofarads per centimeter of wire length. Find the capacitance per meter of length for two 0.2-cm-radius wires spaced 6 cm between centers.
Answer:
8.249 pF per m
Question 2: Convert the formula of above Question 1 to one based upon common logarithms rather than natural logarithms.
Hint: ln N = 2.3026 log N
log N = 0.43429 ln N
Possible answers:
(1) C = 1 / {2.3026 log [(d-r)/r]
(2) C = 1 / {8.289 log [(d-r)/r]
(3) C = 1 / {1.56 log [(d-r)/r]}
(4) C = 1 / {72 log [(d-r)/r]
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This solution shows how to convert a formula based on common logarithms.
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