What equation calculates the equivalent capacitance for n capacitors in series?

What equation calculates the equivalent capacitance for n capacitors in series?

• A. Ceq = C1 + C2 + ... + Cn
• B. Ceq = 1/[(1/C1) + (1/C2) + ... + (1/Cn)]
• C. Ceq = (C1 * C2) / (C1 + C2)
• D. Ceq = C1 * C2 * ... * Cn

Answer: (B)

The equivalent capacitance for capacitors connected in series can be calculated using the formula where the inverse of the equivalent capacitance is equal to the sum of the inverses of the individual capacitances. This relationship arises from the definition of capacitors in series: when capacitors are connected in series, the charge on each capacitor remains the same, but the voltage across the total arrangement becomes the sum of the voltages across each individual capacitor. This is represented mathematically as follows: the total voltage (V_total) is equal to the sum of the voltages across each capacitor (V_1, V_2, …, V_n), which means \(V_{total} = V_1 + V_2 + ... + V_n\). The capacitance is defined as \(C = Q/V\), where Q is the charge and V is the voltage across the capacitor. For capacitors in series, the same charge Q appears on each capacitor. Consequently, the formula for the total capacitance takes the form: \[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_n} \]

The equivalent capacitance for capacitors connected in series can be calculated using the formula where the inverse of the equivalent capacitance is equal to the sum of the inverses of the individual capacitances. This relationship arises from the definition of capacitors in series: when capacitors are connected in series, the charge on each capacitor remains the same, but the voltage across the total arrangement becomes the sum of the voltages across each individual capacitor.

This is represented mathematically as follows: the total voltage (V_total) is equal to the sum of the voltages across each capacitor (V_1, V_2, …, V_n), which means (V_{total} = V_1 + V_2 + ... + V_n). The capacitance is defined as (C = Q/V), where Q is the charge and V is the voltage across the capacitor. For capacitors in series, the same charge Q appears on each capacitor. Consequently, the formula for the total capacitance takes the form:

[

\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_n}

]