Problema Solution
The resistance, R, of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a wire 1200 feet long with a diameter of 0.16 inches is 6848 ohms, what is the resistance of 3600 feet of the same type of wire with a diameter of 0.02 inches? (Leave k in fraction form or to at least 3 decimal place. Round off your final answer to the nearest hundredth.)
Answer provided by our tutors
Since the resistance, R, of a wire varies directly as its length 'l' and inversely as the square of its diameter 'd' we can write
R = k * l / (d^2) where k is a constant.
1 foot = 12 in
For l = 1200 ft = 14400 in and d = 0.16 in the resistance is R1 = 6,848 ohms
R1 = k * 14400 / (0.16^2) => k = (0.16^2) * R1 / 14400
For l = 3600 ft = 43200in and d = 0.02 in R2 = ?
R2 = k * 43200 / (0.02^2)
R2 = ((0.16^2) * 6948 / 14400) * 43200)/ (0.02^2)
R2 = 1,334,016 ohms
R2 = 1,334,000 ohms rounded to the nearest hundred.