In series, which statement about charge and voltage is true?

In series, which statement about charge and voltage is true?

• A. Capacitance decreases in series and the charge is the same on each capacitor, but voltage divides
• B. Capacitance decreases in series and voltage is the same on each capacitor
• C. Capacitance increases in series and charge is the same on each capacitor
• D. Capacitance adds in series and voltage is the same across each capacitor

Answer: (A)

In a series connection, all capacitors carry the same charge because the same amount of charge must flow through the string to reach each capacitor. Because the charges on each capacitor are the same, the overall (equivalent) capacitance of capacitors in series is smaller than any one capacitor, so the series arrangement “decreases” the total capacitance. The voltage across the chain, however, splits among the capacitors: each capacitor has voltage V across it equal to Q/C_i, so smaller capacitance devices take larger shares of the total voltage, and the sum of these voltages equals the total applied voltage. This is why the statement describing decreasing capacitance in series, identical charge on each capacitor, and division of voltage among them is correct.

In a series connection, all capacitors carry the same charge because the same amount of charge must flow through the string to reach each capacitor. Because the charges on each capacitor are the same, the overall (equivalent) capacitance of capacitors in series is smaller than any one capacitor, so the series arrangement “decreases” the total capacitance. The voltage across the chain, however, splits among the capacitors: each capacitor has voltage V across it equal to Q/C_i, so smaller capacitance devices take larger shares of the total voltage, and the sum of these voltages equals the total applied voltage. This is why the statement describing decreasing capacitance in series, identical charge on each capacitor, and division of voltage among them is correct.