Question

six 4.5μf capacitors are connected in parallel
express your answer to two significant figures and include the appropriate units.

part b
what is their equivalent capacitance if connected in series?
express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Calculate equivalent capacitance in parallel

The formula for equivalent capacitance in parallel is \(C_{eq}=\sum_{i = 1}^{n}C_{i}\). Here \(n = 6\) and \(C_{i}=4.5\ \mu F\). So \(C_{eq}=6\times4.5\ \mu F\).

Step2: Calculate equivalent capacitance in series

The formula for equivalent capacitance in series for \(n\) equal - valued capacitors (\(C_{1}=C_{2}=\cdots=C_{n}=C\)) is \(\frac{1}{C_{eq}}=\sum_{i = 1}^{n}\frac{1}{C_{i}}\). Since \(C_{i}=4.5\ \mu F\) and \(n = 6\), then \(\frac{1}{C_{eq}}=\frac{6}{4.5\ \mu F}\), and \(C_{eq}=\frac{4.5\ \mu F}{6}\).

Answer:

• For parallel connection: \(C_{eq}=27\ \mu F\)
• For series connection: \(C_{eq}=0.75\ \mu F\)