Two equal capacitors in series yield an equivalent capacitance of what fraction of a single capacitor?

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Multiple Choice

Two equal capacitors in series yield an equivalent capacitance of what fraction of a single capacitor?

When capacitors are in series, the total capacitance is smaller than either capacitor because the same charge must be stored on each one and the voltage adds up. The formula is 1/Ceq = 1/C1 + 1/C2. If the two capacitors are equal, C1 = C2 = C, so 1/Ceq = 1/C + 1/C = 2/C, which gives Ceq = C/2. So the pair behaves like a single capacitor with half the capacitance. For example, two 10 µF capacitors in series yield Ceq = 5 µF. The other options would apply to different setups: twice as large would be parallel, equal to a single capacitor would be if there was only one capacitor, and a quarter would require four identical capacitors in series (or a similar arrangement).

When capacitors are in series, the total capacitance is smaller than either capacitor because the same charge must be stored on each one and the voltage adds up. The formula is 1/Ceq = 1/C1 + 1/C2. If the two capacitors are equal, C1 = C2 = C, so 1/Ceq = 1/C + 1/C = 2/C, which gives Ceq = C/2. So the pair behaves like a single capacitor with half the capacitance. For example, two 10 µF capacitors in series yield Ceq = 5 µF. The other options would apply to different setups: twice as large would be parallel, equal to a single capacitor would be if there was only one capacitor, and a quarter would require four identical capacitors in series (or a similar arrangement).

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