If three unequal capacitors, initially uncharged, are connected in series across a battery, which of the following statements is true?

1
The equivalent capacitance is greater than any of the individual capacitances. The capacitor with the smallest capacitance has the smallest charge. The largest voltage appears across the capacitor with the smallest capacitance. The capacitor with the largest capacitance has the greatest charge. The largest voltage appears across the capacitor with the largest capacitance.

Your answer is incorrect.

In a series capacitor configuration, each capacitor has the same charge. The voltage across the "ith" one is Vi = Q/Ci The smallest Ci has the largest voltage drop.

The equivalent capacitiance C of the series of capacitors is LESS than any individual one, since
1/C = 1/C1 + 1/C2 + 1/C3

The largest voltage appears across the capacitor with the smallest capacitance. That is the statement you should have chosen

I apologize for the incorrect answer. The correct statement is: The equivalent capacitance is less than any of the individual capacitances. The capacitor with the largest capacitance has the smallest charge. The largest voltage appears across the capacitor with the largest capacitance.

To determine the correct statement, let's review the behavior of capacitors in a series circuit.

When capacitors are connected in series, the total capacitance (C_eq) is given by the reciprocal of the sum of the reciprocals of the individual capacitances (C1, C2, C3):

1 / C_eq = 1 / C1 + 1 / C2 + 1 / C3

From this equation, it is clear that the equivalent capacitance is less than the smallest individual capacitance. Therefore, the first statement is incorrect.

When capacitors are initially uncharged and connected in series to a battery, the same amount of charge (Q) will flow through each capacitor. This is because capacitors in series share the same charge. Therefore, the second statement is incorrect.

The voltage across each capacitor (V) is given by the equation:

V = Q / C

Since the same charge flows through each capacitor, the voltage across each capacitor is inversely proportional to its capacitance. Therefore, the third statement is correct. The largest voltage appears across the capacitor with the smallest capacitance.

Lastly, since the capacitance is inversely proportional to the charge, the capacitor with the smallest capacitance will have the greatest charge. Therefore, the fourth statement is correct. The capacitor with the largest capacitance has the greatest charge.

In summary:
- The equivalent capacitance is less than any of the individual capacitances.
- The capacitor with the smallest capacitance has the greatest charge.
- The largest voltage appears across the capacitor with the smallest capacitance.

Hence, the correct statement is that the largest voltage appears across the capacitor with the smallest capacitance.