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Capacitors

Net Capacitan...

Question

Net Capacitance of three identical in series is $1 μ F$ . What will be their net capacitance, if connected in parallel? Find the ratio of energy stored in the two configurations, if they are both connected to the same source.

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Solution

In series combination,

$\frac{1}{C_{s}} = \frac{1}{C} + \frac{1}{C} + \frac{1}{C}$

$C = 3 C_{s}$

$C = 3 μ F$

When connected in parallel

$C_{p} = 3 C$

$C_{p} = 9 F$

Ratio of energy stored

$\frac{U_{s}}{U_{p}} = \frac{\frac{1}{2} C_{s} V^{2}}{\frac{1}{2} C_{p} V^{2}} = \frac{C_{s}}{C_{p}}$

$U_{s} : U_{p} = 1 : 9$

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