A brand new standard household 9-V battery has about the same potential energy a

Question

A brand new standard household 9-V battery has about the same potential energy as a 2200 lb car at the top of a 1200-ft-high hill. (a) How long will the circuit in the picture run if its voltage source is replaced with a 9-V battery? Assume the 9-V battery is ideal, e.g. zero internal resistance and constant voltage. Now, a 9 V golf cart battery contains about 1000 times more potential energy than a household 9-V battery. (b) How long would it run this circuit? (c) If the golf cart battery was driving this circuit, what would be the current in the 8.00 omega 1.0 omega, and 20.0 omega resistors?

Explanation / Answer

PE=mgh=887.9032*9.8*365.76=3.18*10^6J

R=12+ [(9||5)+(1||7)] || [20+(8||16)] || [(9||18)] =14.22 ohms

So i=V/R=0.633A

a)V^2/R*t=PE

So

t=558266.67 seconds =6.46 days(approx)

b)For 1000 times more PE in golf cart battery

t=55826666.67sec=6461.42 days

c)Current in 20 ohm=current in second branch=(V-12i)/(76/3)=0.055421A

Current in 8 ohm=0.055421*16/24=0.037A

Current in 1 ohm=i(1st branch)*7/8=0.3A

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