You are at the Gas station and you notice your tire is a little Flat. Checking t

Question

You are at the Gas station and you notice your tire is a little Flat. Checking the pressure you a find your tires have only 26 psi. Luckily your car comes equipped with a Superefficient 5 Horsepower DC Air compressor that you can plug into the cigarette lighter and use the Car's battery. For every 800 J of energy put into the compressor the tire is inflated 0.2 psi. How long does it take for the tire to be inflated back up to a safe pressure? By coincidence the gas station has an AC compressor (V_max = 125V) with exactly the same resistance as your DC compressor! This compressor inflates the tire at a rate of 650 J of energy to 0.3 psi. How long does it take to pump up your tire with the Gas Stations Compressor? Before you leave you notice the windshield wiper won't turn and checking the fuse box you find the 15 A fuse connected to the windshield wiper circuit is blown. You don't have any more 15 Amp fuses but you do have several 5 A; 10 A; 20 A; and 30 A fuses. Which one s

Explanation / Answer

a) The optimum level of pressure in the tire should be 35Psi as per standard

Therefore te tire needs 35-26=9Psi more pressure

Now 5 Hp air compressor means =5* 745.7Joules/sec energy= 3728.5joules/sec

that means air compressor introduce  3728.5joules in 1 sec in the tire

Again 800joule power inflates the tire by .2psi

then for 9psi total energy required= 1440joules

For 1440joules energy total time required= 1440/3728.5=.386sec [we consider energy and pressure relation as linear]

b)From standard rules 125v Ac means 15amps rating which means it uses 3/4HP motor

that means energy /sec= 3/4* 745.7 joules/sec for the compressor= 559.275joules/sec

In this case the compressor inflates .3psi for 650jouls

then for 9psi total energy required=1755joules

total time taken=1755/559.275= 3.13sec

c)Higher-amp fuses usually increase the risk of ffire and other issues. Therefore we cannot use 20 or 30amp fuses in this case. These fuses can draw more current but we have to consider the suitability. Therefore 10amp is most sutable for the branch circuit in this case. We can also connect the 5 and 10amp fuses in series in this case.

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