N identical capacitors in series have Ceq equal to C/N. Which expression correctly gives the equivalent capacitance?

N identical capacitors in series have Ceq equal to C/N. Which expression correctly gives the equivalent capacitance?

• A. N C
• B. C
• C. C / N
• D. C / N^2

Answer: (C)

In a series connection, the same charge flows through every capacitor and the voltages add up. For a capacitor, V = Q/C, so each capacitor with capacitance C has V_i = Q/C. With N identical capacitors in series, the total voltage is V_total = N*(Q/C). The equivalent capacitance is defined by Ceq = Q / V_total. Plugging in gives Ceq = Q / [N*(Q/C)] = C/N. So the correct expression is C divided by N. This matches the relationship for identical capacitors in series: the overall capacitance decreases by a factor of N.

In a series connection, the same charge flows through every capacitor and the voltages add up. For a capacitor, V = Q/C, so each capacitor with capacitance C has V_i = Q/C. With N identical capacitors in series, the total voltage is V_total = N*(Q/C). The equivalent capacitance is defined by Ceq = Q / V_total. Plugging in gives Ceq = Q / [N*(Q/C)] = C/N. So the correct expression is C divided by N. This matches the relationship for identical capacitors in series: the overall capacitance decreases by a factor of N.