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2 answers:
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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
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
and since Ceq must be equal to 4 C1, we can write
from which we find
The maximum efficiency is 10%
Explanation:
The maximum efficiency of a machine is given by:
where
is the temperature of the hot reservoir
is the temperature of the cold reservoir
For the machine in this problem, we have:
is the temperature of the hot reservoir
is the temperature of the cold reservoir
substituting, we find the max efficiency:
So, the efficiency is 0.10 (10%).
Learn more about temperature:
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