Two capacitors C1 and C2 are connected in series; what is the total capacitance C_total?

Two capacitors C1 and C2 are connected in series; what is the total capacitance C_total?

• A. C_total = C1 + C2
• B. C_total = (C1 C2)/(C1 + C2)
• C. 1/C_total = 1/C1 + 1/C2
• D. C_total = min(C1, C2)

Answer: (C)

In a series arrangement, the same charge flows onto each capacitor, so the charges on both C1 and C2 are equal: Q = C1 V1 = C2 V2. The total voltage across the combination is the sum of the individual voltages: V_total = V1 + V2. Expressing the voltages in terms of Q gives V1 = Q/C1 and V2 = Q/C2, so V_total = Q(1/C1 + 1/C2). The overall capacitance is defined by C_total = Q / V_total, which leads to C_total = 1 / (1/C1 + 1/C2). This reciprocal-sum form is exactly the relationship for capacitors in series and is equivalent to C_total = (C1 C2)/(C1 + C2). The key takeaway is that the total capacitance in series is found by the sum of the reciprocals, which yields a value smaller than either individual capacitor.

In a series arrangement, the same charge flows onto each capacitor, so the charges on both C1 and C2 are equal: Q = C1 V1 = C2 V2. The total voltage across the combination is the sum of the individual voltages: V_total = V1 + V2. Expressing the voltages in terms of Q gives V1 = Q/C1 and V2 = Q/C2, so V_total = Q(1/C1 + 1/C2). The overall capacitance is defined by C_total = Q / V_total, which leads to C_total = 1 / (1/C1 + 1/C2). This reciprocal-sum form is exactly the relationship for capacitors in series and is equivalent to C_total = (C1 C2)/(C1 + C2). The key takeaway is that the total capacitance in series is found by the sum of the reciprocals, which yields a value smaller than either individual capacitor.