Answer: 33.5 x 10⁻⁶ C
Explanation:
By definition, the capacitance is the relationship between the charge on one of the plates (assuming it's a capacitor) and the voltage between them:
C = Q / V
Now, it can be showed that we can find the capacitance of a parallel-plate capacitor, taking into account the geometry and the dielectric material only, as follows:
C = ε A /d = ε₀ εr A / d
If the dielectric is air, we can assume εr = 1
If the space between plates is filled with a dielectric of dielectric constant 7.74, the new value for capacitance (regarding the former value) must be 7.74 times larger, as A and d didn't change.
So, in order to produce the same potential difference between the plates, we need to increase the charge, exactly 7.7 times:
Q = 7.7. 4.33 . 10⁻⁶ C = 33.5 . 10⁻⁶ C
