A student has a battery with emf ε and two uncharged capacitors with capacitances 2C and 3C. The student also has plenty of connecting wires. What is the highest voltage that can be obtained using this equipment?

If we charge one of the two capacitors (labeled by C1) up to the battery voltage ε and connect it in series with the battery afterward, the voltage at the ends will be 2ε. When these two are connected to the second capacitor (labeled by C2), the charge will transfer to it in accordance with Kirchhoff’s second law. By repeatedly charging C1 to the battery voltage and connecting it with the battery and C2 the same way, we can charge C2 up to the 2ε, as we will prove.

If you have two capacitors and one battery with emf...

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