Final answer:
The impedance of a capacitor decreases with increasing frequency, making the statement false. Capacitance is a fixed value that does not depend on the charge, and the energy stored in a capacitor increases when a dielectric material is placed between the plates.
Step-by-step explanation:
The impedance of a capacitor does not increase with increasing frequency. On the contrary, the impedance decreases as the frequency increases. This is because the impedance of a capacitor (Z) is inversely proportional to the frequency (f) of the signal passing through it, which can be described by the formula Z = 1/(2πfC), where C is the capacitance. As the frequency increases, the value of 1/(2πfC) becomes smaller, indicating a lower impedance. Therefore, the statement is false.
Furthermore, it's important to note that the capacitance of a capacitor is a measure of its ability to store charge and is determined by factors such as the area of the plates, the distance between them, and the type of dielectric material used. The capacitance itself does not depend on the applied voltage or the charge residing on it, but the amount of charge stored does.
The statement that the capacitance value is zero if the plates are not charged is false; capacitance is a physical property of the capacitor itself that is not dependent on the amount of charge.
If the plates of a capacitor have different areas and are connected across a battery, they will not acquire the same charge. The charge distribution will be influenced by the geometry of the plates among other factors.
Placing a dielectric between the plates of a capacitor will increase the energy stored by the capacitor, because the dielectric increases the capacitance which in turn increases the energy, given by the equation U = (1/2)CV² where U is the energy, C is the capacitance, and V is the voltage.