For N identical capacitors connected in series, the equivalent capacitance is Ceq = C/N.

For N identical capacitors connected in series, the equivalent capacitance is Ceq = C/N.

• A. C/N
• B. N C
• C. C
• D. N/C

Answer: (A)

In a series connection, the same charge flows through every capacitor and the voltages add up. The reciprocal rule for series capacitors says 1/Ceq = sum of 1/Ci. If all capacitors are identical with capacitance C, this becomes 1/Ceq = N*(1/C), so Ceq = C/N. This shows why adding more capacitors in series lowers the total capacitance: the total voltage is shared across more devices while the same charge passes through each, reducing the effective storage for a given voltage. The other expressions don’t fit the situation. C/N correctly reflects the series reduction in capacity as N grows. C would imply no change with N, which isn’t true in series. N*C would be the result if capacitors were in parallel, not in series. N/C has the wrong units (newtons per coulomb, not farads).

In a series connection, the same charge flows through every capacitor and the voltages add up. The reciprocal rule for series capacitors says 1/Ceq = sum of 1/Ci. If all capacitors are identical with capacitance C, this becomes 1/Ceq = N*(1/C), so Ceq = C/N. This shows why adding more capacitors in series lowers the total capacitance: the total voltage is shared across more devices while the same charge passes through each, reducing the effective storage for a given voltage.

The other expressions don’t fit the situation. C/N correctly reflects the series reduction in capacity as N grows. C would imply no change with N, which isn’t true in series. N*C would be the result if capacitors were in parallel, not in series. N/C has the wrong units (newtons per coulomb, not farads).