The following values may be useful for this problem: copper = 1.72 · 10-8 · m ca

Question

The following values may be useful for this problem:

copper = 1.72 · 10-8 · m
carbon = 3500 · 10-8 · m

You have a 15 mm long cylindrical carbon resistor, with a cross-section of radius 15·10-6 m.

a.) What is its resistance?


b.) The resistor is now connected to a 120 V battery. How much energy is dissipated to heat per second in this one resistor?
___W

c.) Explain why it is so important to think about ventilation and/or a cooling fan when building any kind of machine.



We usually approximate that wires (made out of conductors) have no resistance, and any resistance in a circuit is due to special "resistors" that we put into the circuit. In reality, every part of the circuit (even a conductor) has some resistance-- it's just that some parts of the circuit have a negligible resistance compared to others. (For instance, compare the resistances in #7 above.)

d.) If the copper wire we use to connect the carbon resistor to the battery has a cross-sectional radius of 14·10-6 m and a total length of 15 cm, how much resistance is added to the circuit by the wire itself?

(Is this resistance somewhat negligible, compared to the carbon resistor?)

Explanation / Answer

given le ngth of resaistor = 15mm = 15 * 10^-3m radius of resistor = r = 15 * 10^-6m     cross sectional area of resistor = A = 2prL = 2 * 3.14 * 15 * 10^-6m15 * 10^-3m                                                                   = 1.4 * 10^-6m^2     resistance R = ? L/A                         = 3500 * 10^-8Om * 15 * 10^-3m/1.4 * 10^-6m^2                          = 0.37O     volatage conneted to resistor = v = 120v       p = E/t          E = pt             = V2/R * t            = (120v)2/0.37O * 1sec            =3.89 * 104W d)if copper wire is connected le ngth of resaistor = 15cm = 15 * 10^-2m radius of resistor = r = 14 * 10^-6m     cross sectional area of resistor = A = pr2 = 3.14 * (14 * 10^-6m)2                                                                   = 6.15 * 10^-10m^2     resistance R = ? L/A                         = 1.72 * 10^-8Om * 15 * 10^-2m/6.15 * 10^-10m^2                          = 4.19O radius of resistor = r = 14 * 10^-6m     cross sectional area of resistor = A = pr2 = 3.14 * (14 * 10^-6m)2                                                                   = 6.15 * 10^-10m^2     resistance R = ? L/A                         = 1.72 * 10^-8Om * 15 * 10^-2m/6.15 * 10^-10m^2                          = 4.19O

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