So repair a power supply for a stereo amplifier, an...

So repair a power supply for a stereo amplifier, an electronics technician needs a $100-\mu \mathrm{F}$ capacitor capable of withstanding a potential difference of 90 $\mathrm{V}$ between the plates. The immediately available supply is a box of five $100-\mu \mathrm{F}$ capacitors, each having a maximum voltage capability of 50 $\mathrm{V}$ . Can the technician use one of the capacitors from the box? Can she substitute a combination of these capacitors that has the proper electrical characteristics? Will the technician use all the capacitors in the box? Explain your answers. In a combination of capacitors, what will be the maximum voltage across each of the capacitors used?

Key Concepts

Voltage Distribution in Series-Connected Capacitors

In a series configuration of identical capacitors, the total applied voltage is equally divided among the capacitors. This principle ensures that each capacitor only experiences a fraction of the total voltage, which is crucial when substituting for a higher voltage-rated capacitor with several lower voltage-rated ones.

Component Substitution in Circuit Design

This concept involves replacing a component with one or more components arranged in a particular configuration to meet specific circuit requirements. In the context of this problem, individual capacitors with lower voltage ratings can be combined in series to match both the needed capacitance and the higher voltage rating required by the circuit.

Equivalent Capacitance

When capacitors are connected in series, the effective or equivalent capacitance of the configuration is less than that of any individual capacitor. This reduction in capacitance must be taken into account, as it affects the performance of the circuit and may require adjustments to achieve the desired capacitance value.

Series Combination of Capacitors

Connecting capacitors in series increases the overall voltage tolerance of the arrangement. When capacitors are connected in series, the applied voltage divides evenly across them (provided they have identical capacitance), allowing the series string to handle a higher total voltage than any individual capacitor’s rating.

Capacitor Voltage Rating

This concept refers to the maximum voltage that a capacitor can safely handle without risk of failure. In circuit design, it is essential to choose a capacitor whose voltage rating exceeds the operational maximum to ensure reliability and safety.

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