The capacities of three capacitors are in the ratio 1: 2: 3....

The capacities of three capacitors are in the ratio $1: 2: 3$. Their equivalent capacity when connected in parallel is $(60 / 11) \mathrm{F}$ more then that when they are connected in series. The individual capacitors are of capacities in $\mu \mathrm{F}$ (A) $4,6,7$ (B) $1,2,3$ (C) $1,3,6$ (D) $2,3,4$

Key Concepts

Capacitors in Parallel

When capacitors are connected in parallel, their equivalent capacitance is simply the sum of their individual capacitances. This concept is fundamental because each capacitor in parallel shares the same voltage, and the total stored charge is the sum of charges from each capacitor, making the analysis straightforward.

Capacitors in Series

In a series configuration, the equivalent capacitance is found by taking the reciprocal of the sum of the reciprocals of the individual capacitances. This occurs because the same charge flows through each capacitor, while the voltage divides among them. The series connection results in a lower overall capacitance compared to any individual capacitor in the series.

Ratio and Proportional Reasoning

When components like capacitors are defined in terms of ratios, it implies that each individual component can be expressed as a multiple of a common variable. This technique simplifies the analysis and calculation by reducing the problem to solving for that common variable, which then gives the actual values of each component.

Algebraic Equation Setup

Setting up and solving algebraic equations is essential for relating the different expressions for equivalent capacitance in series and parallel configurations. By representing the capacitor values with a variable that adheres to a given ratio and equating the difference between the series and parallel combinations to a specified value, one can solve for the unknown variable and determine the individual capacitance values.

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