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 thanthe 12-V systems used in automobiles, even though the electricalpower requirements are roughly the same. This is because a 24-Vsystem uses thinner wires and therefore weighs less. Explain thisreasoning.
c. Show why the internal resistance of a source can bedetermined by dividing the open-circuit voltage by theshort-circuit current.
d. Assuming each source has a small internal resistance, whichcircuit(s) would light up the light bulb? Which circuit(s) do youthink would be likely to cause damage to the ammeter orvoltmeter?
2. You have a battery, a voltmeter, and an ammeter, and you areasked to find the resistance perunit-length ?′ of a long spool ofwire. 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 inseries and it reads 9.6 A. You then connect a 50 m length of wireand the ammeter now reads 4.1 A.
a. What is the resistance per-unit-length of the wire andinternal 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 ofpower dissipated within the internal resistance of the batteryrelative to the total power dissipated? Is this percentage larger,smaller, or the same as for the 50 m wire? 3. Consider thefollowing circuit containing two sources, each with an internalresistance of 5 ï—, and two load resistors, being 40 ï— and 100 ï—. a.How much current flows through this circuit and in what directiondoes 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 isit 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 thetotal 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 effectof the internal resistances.)
4. The average bulk resistivity inside the human body is about 5Ω.m. The surface resistance of the skin varies considerably, fromaround 100,000 Ω for dry skin to 1000 Ω for wet skin. If the skinis broken and soaked in salt water, the skin resistance will evenapproach zero. Furthermore, the skin resistance can break down whenvoltages are high (above 500 V) or when voltages are changing (likeunder alternating current conditions). You can model the conductingpath between the hands as three resistors in series. The first andthird resistors represent the skin resistance while the secondresistor represents the internal resistance of the body and can bemodeled as a cylinder of diameter 10 cm and length 1.6 m.
a. Calculate the resistance between the hands for dry skin, wetskin, and broken soaked skin.
b. What potential difference would be needed for a lethal shockcurrent of 100 mA in each of the three cases in part a (ignoringbreakdown)?
c. Considering the chart below (taken from C. F. Dalziel,“Deleterious effects of electric shock,†1961), how bad would aworst-case shock be from a 12 V DC car battery, your 50 V DC homephone line, and a 120 V 60 Hz wall outlet (i.e. with broken soakedskin)? Warning, don’t test any of these situations out at home!Despite your findings, there have been cases where people have diedof an electric shock from a car battery. DC 60 Hz AC 10 kHz ACEffect Men Women Men Women Men Women Slight sensation on hand 1 mA0.6 mA 0.4 mA 0.3 mA 7 mA 5 mA Perception threshold, median 5.2 mA3.5 mA 1.1 mA 0.7 mA 12 mA 8 mA Shock, not painful and muscularcontrol 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 mAPainful shock, let-go threshold, median 76 mA 51 mA 16 mA 10.5 mA75 mA 50 mA Painful and severe shock, breathing difficult, muscularcontrol lost by 99.5% 90 mA 60 mA 23 mA 15 mA 94 mA 63 mA Possibleventricular fibrillation 500 mA 500 mA 100 mA 100 mA n/a n/a
