Question

4.3.2 test (cst): electromagnets
the table shows the sizes of four different types of electrical wire. if the
resistance of the four wires is ranked from highest to lowest, how does the
resistance of a wire used to power light fixtures rank?
wire diameter, mm use
4.1154 stove tops
2.5882 clothes dryers
1.6277 light fixtures
1.0237 lamp cords
a. second
b. fourth
c first

Explanation:

Step1: Recall the relationship between resistance and wire diameter

Resistance \( R=
ho\frac{l}{A} \), where \( A = \frac{\pi d^{2}}{4} \) (\( d \) is the diameter). So \( R\propto\frac{1}{d^{2}} \). Smaller diameter means higher resistance.

Step2: Compare the diameters

Given diameters: \( d_{stove}=4.1154\mathrm{mm}\), \(d_{dryer} = 2.5882\mathrm{mm}\), \(d_{light}=1.6277\mathrm{mm}\), \(d_{lamp}=1.0237\mathrm{mm}\).
Arranging diameters from smallest to largest: \(d_{lamp}Since \( R\propto\frac{1}{d^{2}} \), arranging resistances from highest to lowest: \(R_{lamp}>R_{light}>R_{dryer}>R_{stove}\).

Answer:

A. Second