Question

Answer the following short questions.

a. A rectangular block has a resistivity of ? and resistance of ?. If we scale it up in size by a factor of 2 in every direction, what is the new resistivity and resistance as a function of ? and ??

b. Small aircraft often use 24-V electrical systems rather than the 12-V systems used in automobiles, even though the electrical power requirements are roughly the same. This is because a 24-V system uses thinner wires and therefore weighs less. Explain this reasoning.

c. Show why the internal resistance of a source can be determined by dividing the open-circuit voltage by the short-circuit current.

d. Assuming each source has a small internal resistance, which circuit(s) would light up the light bulb? Which circuit(s) do you think would be likely to cause damage to the ammeter or voltmeter?

2. You have a battery, a voltmeter, and an ammeter, and you are asked to find the resistance perunit-length ?′ of a long spool of wire. You connect the voltmeter to the battery and it reads 3.2 V. You connect the battery to 20 m of the wire with the ammeter in series and it reads 9.6 A. You then connect a 50 m length of wire and the ammeter now reads 4.1 A.

a. What is the resistance per-unit-length of the wire and internal resistance of the battery?

b. If the wire is made from copper, with a resistivity of ? = 1.7×10−8 Ω⋅m, what is its diameter? c. What is the percentage of power dissipated within the internal resistance of the battery relative to the total power dissipated? Is this percentage larger, smaller, or the same as for the 50 m wire? 3. Consider the following circuit containing two sources, each with an internal resistance of 5 , and two load resistors, being 40  and 100 . a. How much current flows through this circuit and in what direction does it flow? b. What is the potential at a relative to ground? What is the potential at b relative to ground?

c. Where in the circuit is the potential the highest? Where is it the lowest?

d. Calculate the total power dissipated in both load resistors. 2 e. If the 100 Ω resistor is replaced by a short circuit, is the total power absorbed by the 40 Ω resistor greater than, equal to, or less than the total power initially absorbed by both resistors? f. How much power is supplied by each source? (Include the effect of the internal resistances.)

4. The average bulk resistivity inside the human body is about 5 Ω.m. The surface resistance of the skin varies considerably, from around 100,000 Ω for dry skin to 1000 Ω for wet skin. If the skin is broken and soaked in salt water, the skin resistance will even approach zero. Furthermore, the skin resistance can break down when voltages are high (above 500 V) or when voltages are changing (like under alternating current conditions). You can model the conducting path between the hands as three resistors in series. The first and third resistors represent the skin resistance while the second resistor represents the internal resistance of the body and can be modeled as a cylinder of diameter 10 cm and length 1.6 m.

a. Calculate the resistance between the hands for dry skin, wet skin, and broken soaked skin.

b. What potential difference would be needed for a lethal shock current of 100 mA in each of the three cases in part a (ignoring breakdown)?

c. Considering the chart below (taken from C. F. Dalziel, “Deleterious effects of electric shock,” 1961), how bad would a worst-case shock be from a 12 V DC car battery, your 50 V DC home phone line, and a 120 V 60 Hz wall outlet (i.e. with broken soaked skin)? Warning, don’t test any of these situations out at home! Despite your findings, there have been cases where people have died of an electric shock from a car battery. DC 60 Hz AC 10 kHz AC Effect Men Women Men Women Men Women Slight sensation on hand 1 mA 0.6 mA 0.4 mA 0.3 mA 7 mA 5 mA Perception threshold, median 5.2 mA 3.5 mA 1.1 mA 0.7 mA 12 mA 8 mA Shock, not painful and muscular control not lost 9 mA 6 mA 1.8 mA 1.2 mA 17 mA 11 mA Painful shock, muscular control lost by 0.5% 62 mA 41 mA 9 mA 6 mA 55 mA 37 mA Painful shock, let-go threshold, median 76 mA 51 mA 16 mA 10.5 mA 75 mA 50 mA Painful and severe shock, breathing difficult, muscular control lost by 99.5% 90 mA 60 mA 23 mA 15 mA 94 mA 63 mA Possible ventricular fibrillation 500 mA 500 mA 100 mA 100 mA n/a n/a

Answer 1

for question (d) , figure is required.

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