Question

2.3 Your friend tells you a story of their roommate being tired of everyone making a mess in the microwave, so he moves it to his room. Because of all of the electronics in his room, he runs a 250 foot, 14 gauge extension cord from the living room to run the microwave. The specifications on the microwave state when it is plugged directly into the 120 volt wall outlet, it will draw 16 amps. How many volts will be delivered to the microwave when it is plugged in series with the extension cord? (Numbers you might need: 100 feet = 30.48 meters, resistivity of copper p=1.68*108 ohm · m, diameter of 14 gauge wire = 1.628 mm) (10 points)

Answer 1

Solution:

Resistance in cord

$R_{c}=\rho \frac{l}{A}=\rho \frac{l}{\frac{\pi d^{2}}{4}}$

$R_{c}=\left ( 1.68\times 10^{-8}\Omega -m \right ) \frac{\left (\frac{250ft\times 30.48m }{100ft} \right )}{\frac{\pi \left ( 1.628\times 10^{-3}m \right )^{2}}{4}}$

Rc = 0.61922

Overall resistance,

$R=\frac{\varepsilon }{I}$

$R=\frac{120V }{16A}=7.5\Omega$

The resistances are combined in series

$R=R_{c}+R_{m}$

$7.5\Omega =0.619\Omega +R_{m}$

$R_{m}=6.881\Omega$

The voltage drop across microwave

$V_{m}=IR_{m}$

$V_{m}=\left ( 16A \right )\left ( \Omega 6.881 \right )$

$V_{m}=110.1V$