According to its design specification, the timer circuit...

According to its design specification, the timer circuit delaying the closing of an elevator door is to have a capacitance of $32.0 \mu F$ between two points $A$ and $B$. (a) When one circuit is being constructed, the inexpensive capacitor installed between these two points is found to have capacitance $94.8 \mu \mathrm{F}$. To meet the specification, one additional capacitor can be placed between the two points. Should it be in series or in parallel with the $34.8-\mu$ Fapacitor? What should be its capacitance? (b) The next circuit comes down the assembly line with capacitance $29.8 \mu \mathrm{F}$ between $A$ and $B .$ What additional capacitor should be installed in series or in parallel in that circuit, to meet the specification?

According to its design specification, the timer circuit delaying the closing of an elevator door is to have a capacitance of $32.0 \mu F$ between two points $A$ and $B$.
(a) When one circuit is being constructed, the inexpensive capacitor installed between these two points is found to have capacitance $94.8 \mu \mathrm{F}$. To meet the specification, one additional capacitor can be placed between the two points. Should it be in series or in parallel with the $34.8-\mu$ Fapacitor? What should be its capacitance?
(b) The next circuit comes down the assembly line with capacitance $29.8 \mu \mathrm{F}$ between $A$ and $B .$ What additional capacitor should be installed in series or in parallel in that circuit, to meet the specification?

Key Concepts

Equivalent Capacitance Calculation

Calculating equivalent capacitance involves using formulas specific to series and parallel connections. In series, it is determined by the reciprocal formula, and in parallel, by direct summation. Mastering these calculations is crucial for modifying circuit designs to meet precise specifications, such as tuning the time delay in electronic circuits.

Parallel Combination of Capacitors

In a parallel configuration, the equivalent capacitance is simply the sum of the individual capacitances. This method increases the overall capacitance and is used when the target capacitance value is higher than that of any single available capacitor, allowing for flexibility in achieving design specifications.

Series Combination of Capacitors

When capacitors are connected in series, the total or equivalent capacitance is given by the reciprocal of the sum of the reciprocals of the individual capacitances. This configuration results in an overall capacitance that is lower than any individual capacitance in the series, which is particularly useful when a circuit requires a specific, reduced capacitance value.

Capacitance

Capacitance is a measure of a capacitor's ability to store electrical charge per unit voltage, usually expressed in farads. The value of capacitance determines how a capacitor behaves in a circuit, particularly in timing, filtering, and energy storage applications, making it a fundamental parameter in circuit design.

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