The capacitors of capacitance 4 μF, 6 μF and 12 μF are connected first in series and then in par

step 1 In this problem, when they are in when it is in series, I can write the value of 1 by C as 1 by

The capacitors of capacitance 4 μF, 6 μF and 12 μF are...

The capacitors of capacitance $4 \mu \mathrm{F}, 6 \mu \mathrm{F}$ and $12 \mu \mathrm{F}$ are connected first in series and then in parallel. What is the ratio of equivalent capacitance in the two cases?
(A) $2: 3$
(B) $11: 1$
(C) $1: 11$
(D) $1: 3$

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Key Concepts

Parallel Connection of Capacitors

In a parallel configuration, the capacitors are connected with all their positive terminals linked together and all their negative terminals linked together, ensuring that each capacitor experiences the same voltage. The equivalent capacitance in this case is the sum of the individual capacitances, yielding a higher total capacitance.

Ratio Calculation

Calculating a ratio involves comparing the relative sizes of two quantities. In circuit problems, it often serves to contrast outcomes such as the equivalent capacitance of different configurations by establishing a proportional relationship between them.

Capacitors

Capacitors are electronic components that store energy in an electric field when a voltage is applied. Their ability to store charge is measured by capacitance, which is a fundamental property in circuit analysis.

Series Connection of Capacitors

In a series configuration, capacitors are connected one after another so that the same charge passes sequentially through each. The overall or equivalent capacitance is found by taking the reciprocal of the sum of the reciprocals of the individual capacitances, resulting in a value that is lower than any single capacitor in the chain.

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