The circuit shown on the right has two capacitors of unequal capacitances connec

Question

The circuit shown on the right has two capacitors of unequal capacitances connected in series and connected to a battery. Indicate whether each of the statements below is true or false, and for each false statement write a correct one. Both capacitors are accumulate the same amount of charge on their plates. The potential difference across each capacitor is the same. The sum of the individual potential differences across each capacitor is equal to the potential difference supplied by the battery.

Explanation / Answer

A. True. The charge is the same. You can think of it in terms of current, since current is the time derivative of charge. The current in a single loop is the same at every part of the loop because of Kirchhoff's Current Rule -- the current entering a node and a current leaving a node are equal. A node is where two or more circuit elements connect. In a single loop circuit, every node has only one path into it and one path out of it. Thus, current is equal everywhere. Thus, the charge is the same at each point in the circuit, including the capacitors. B. False. The potential difference is the voltage drop across an object. The voltage across a capacitor is V=Q/C. Since charge is the same but the capacitance is different, both capacitors will have different voltages across them. C. True. Kirchhoff's Voltage Law -- the sum of the voltage rises and voltage drops is zero. The battery causes a voltage rise, the capacitors cause a voltage drop. Both must be equal. Although the individual voltages across the capacitors are different, their sum will always equal the voltage generated by the voltage source.

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