What is the relative size and composition of the universe, a galaxy, and a solar system? Is the universe endless?
2 answers:
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(a) 800 V
The capacitance of a parallel-plate capacitor is given by
where
is the vacuum permittivity
A is the area of each plate
d is the separation between the plates
We see that the capacitance is inversely proportional to the separation, d: in this problem, the separation between the plates is doubled (2d), so the capacitance will become half of its original value:
The potential difference between the plates is related to the capacitance by
(1)
where Q is the charge stored on the plate. In this problem, the charge is not changed: therefore, the new potential difference is
So, the potential difference has doubled, and since the initial value was
V = 400 V
The new value is
V' = 2(400) = 800 V
(b) The charge will decrease by a factor 2
As before, the plate spacing is doubled, so according to the equation
Then the capacitance is halved again:
This time, however, the voltage is held constant. We can rewrite the eq.(1) as
Q = CV
And since V has not changed, we can find what is the new charge stored in the capacitor:
So, the charge will be halved compared to the original charge.