Circuit of the paradox, showing initial voltages before the switch is closed
The two capacitor paradox or capacitor paradox is a paradox, or counterintuitive thought experiment, in electric circuit theory.[1][2] The thought experiment is usually described as follows:
Two identical capacitors are connected in parallel with an open switch between them. One of the capacitors is charged with a voltage of , the other is uncharged. When the switch is closed, some of the charge on the first capacitor flows into the second, reducing the voltage on the first and increasing the voltage on the second. When a steady state is reached and the current goes to zero, the voltage on the two capacitors must be equal since they are connected together. Since they both have the same capacitance the charge will be divided equally between the capacitors so each capacitor will have a charge of and a voltage of . At the beginning of the experiment the total initial energy in the circuit is the energy stored in the charged capacitor:
At the end of the experiment the final energy is equal to the sum of the energy in the two capacitors
Thus the final energy is equal to half of the initial energy . Where did the other half of the initial energy go?
^Levine, Richard C. (December 1967). "Apparent Nonconservation of Energy in the Discharge of an Ideal Capacitor". IEEE Transactions on Education. 10 (4). Institute of Electrical and Electronics Engineers: 197–202. Bibcode:1967ITEdu..10..197L. doi:10.1109/TE.1967.4320288. ISSN 1557-9638.
^McDonald, Kirk T. (11 January 2018). "A Capacitor Paradox". Physics Dept., Princeton University. Retrieved 12 June 2018.
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