Question
What would the capacitance of a capacitor with the same total internal energy as the car battery in Example 19.1 have to be? Can you explain why we use batteries instead of capacitors for this application?
Final Answer
. This capacitance is enormous, and probably impossible to manufacture.
Solution video
OpenStax College Physics for AP® Courses, Chapter 19, Problem 40 (Test Prep for AP® Courses)
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Video Transcript
This is College Physics Answers with Shaun Dychko. The battery in the car of example [19.1] has an energy of 7.20 times 10 to the 5 joules stored in it, its voltage is 12.0 volts and the question here is what would the capacitance of a capacitor need to be to have the same energy? So we express the energy stored in a capacitor in terms of capacitance and voltage so we have capacitance times voltage squared over 2 and we solve this for C by multiplying both sides by 2 over V squared. So capacitance then is 2 times the energy stored divided by the voltage squared. So that's 2 times 7.20 times 10 to the 5 joules divided by 12.0 volts squared, which is 1.00 times 10 to the 4 farads. This is an enormous number when it comes to capacitance and it's probably impossible to manufacture such a high capacitance capacitor.