Round to the nearest tenth unless indicated otherwise.
-The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of $0.1$ inch has a resistance of 3 ohms What would the resistance be for a 21 foot length, with diameter $0.01$ inch, of the same kind of wire ?
A) $308 \mathrm { ohms }$
B) $327 \mathrm { ohms }$
C) $312.5 \mathrm { ohms }$
D) $315 \mathrm { ohms }$

Question

Quizplus · Accepted Answer

The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire.$$R = \frac{kL}{d^2}$$where:* R is the resistance in ohms* k is a constant* L is the length of the wire in feet* d is the diameter of the wire in inchesWe are given that a 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms. We can use this information to find the value of k:$$3 = \frac{k(20)}{(0.1)^2}$$$$k = 0.015$$Now we can use the value of k to find the resistance of a 21 foot length of wire with a diameter of 0.01 inch:$$R = \frac{kL}{d^2}$$$$R = \frac{0.015(21)}{(0.01)^2}$$$$R = 315 \mathrm { ohms }$$

Round to the Nearest Tenth Unless Indicated Otherwise 0.10.10.1 Inch Has a Resistance of 3 Ohms What Would the of a Wire

Round to the Nearest Tenth Unless Indicated Otherwise $0.1$ Inch Has a Resistance of 3 Ohms What Would the of a Wire