Acircuit contains a single 270-pf capacitor hooked across a battery. it is desired to store four times as much energy in a combination of two capacitors by adding a single capacitor to this one. what would this value be

The energy stored by a system of capacitors is given by

where Ceq is the equivalent capacitance of the system, and V is the voltage applied.

In the formula, we can see there is a direct proportionality between U and C. This means that if we want to increase the energy stored by 4 times, we have to increase C by 4 times, if we keep the same voltage.

Calling  the capacitance of the original capacitor, we can solve the problem by asking that, adding a new capacitor with , the new equivalent capacitance of the system  must be equal to . If we add the new capacitance X in parallel, the equivalent capacitance of the new system is the sum of the two capacitance

and since Ceq must be equal to 4 C1, we can write

from which we find

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