Question

When capacitors with equal values are connected in series, how can the total capacitance of the circuit be calculated?

Option 1: The total capacitance is equal to the value of one capacitor multiplied by the number of total capacitors in the series.

Option 2: The total capacitance is equal to the value of one capacitor divided by the number of total capacitors in the series.

Option 3: The total capacitance is equal to the sum of the capacitance values of all the capacitors in the series.

Option 4: The total capacitance is equal to the square root of the product of the capacitance values of all the capacitors in the series.

Answer 1

The total capacitance of equal-value capacitors in series is the value of one capacitor divided by the number of capacitors.

Step-by-step explanation:

When capacitors with equal values are connected in series, the total capacitance of the circuit can be calculated using a specific formula. The correct calculation is not to multiply or sum up the capacitance values, nor to take a square root of any products. Instead, for capacitors in series, the total capacitance is found by taking the reciprocal of the sum of the reciprocals of each capacitor's capacitance. Mathematically, for capacitors C1, C2, ..., Cn connected in series, the equation is 1/Cs = 1/C1 + 1/C2 + ... + 1/Cn, which always results in a total capacitance (Cs) that is less than any of the individual capacitances. Therefore, Option 2 is the closest to the actual method; the total capacitance is the reciprocal of the sum of the reciprocals of the individual capacitance values, and for capacitors with equal values, it simplifies to the value of one capacitor divided by the number of total capacitors in the series.