Parallel Plate Capacitor: Practice Problem & Solution
It is required to construct a \(10\text{ \mu F}\) capacitor which can be connected across a \(200\text{ V}\) battery. Capacitors of capacitance \(10\text{ \mu F}\) are available but they can withstand only \(50\text{ V}\). Design a combination which can yield the desired result.
Solution Explained:
To solve this problem, we apply the core principles of Parallel Plate Capacitor. Understanding the underlying formula is key to arriving at the correct answer below:
To withstand \(200\text{ V}\) using \(50\text{ V}\) capacitors, \(4\) capacitors must be in series (\(4 \times 50 = 200\text{ V}\)). Each series combination has \(C_{eq} = 10/4 = 2.5\text{ \mu F}\). To get \(10\text{ \mu F}\) total, \(10/2.5 = 4\) such series combinations must be in parallel. Thus, 4 capacitors in series, and 4 such combinations in parallel.
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