1.;A capacitor has a capacitance of 8.0 microFarad with air between its plates. Determine its capacitance when a dielectric with dielectric constant 6.0 is placed between its plates. 2. What is the charge on a 300 pF capacitor when it is charged to a voltage of 1.0 kV? 3. A certain parallel-plate capacitor consists of two plates, each with area 200 cm² , separated by a 0.40 cm air gap. (a) Compute its capacitance. (b) If the capacitor is connected across a 500 V source, find the charge on it, the energy stored in it, and the value of E between the plates. (c) If a liquid with K = 2.60 is poured between the plates so as to fill the air gap, how much additional charge will flow onto the capacitor from the 500 V source?

Initial capacitance with air, $C_0 = 8.0 \text{ µF}$.
Dielectric constant, $K = 6.0$.

The capacitance $C$ with a dielectric is given by $C = K C_0$.

The capacitance with the dielectric is $\boxed{48.0 \text{ µF}}$.

2. What is the charge on a 300 pF capacitor when it is charged to a voltage of 1.0 kV?

Capacitance, $C = 300 \text{ pF} = 300 \times 10^{-12} \text{ F}$.
Voltage, $V = 1.0 \text{ kV} = 1.0 \times 10^3 \text{ V}$.

The charge $Q$ on a capacitor is given by $Q = CV$.

The charge on the capacitor is $\boxed{3.0 \times 10^{-7} \text{ C}}$.

3. A certain parallel-plate capacitor consists of two plates, each with area 200 cm² , separated by a 0.40 cm air gap.

(a) Compute its capacitance.

(b) If the capacitor is connected across a 500 V source, find the charge on it, the energy stored in it, and the value of E between the plates.

(c) If a liquid with K = 2.60 is poured between the plates so as to fill the air gap, how much additional charge will flow onto the capacitor from the 500 V source?

Given values:
Area, $A = 200 \text{ cm}^2 = 200 \times (10^{-2} \text{ m})^2 = 200 \times 10^{-4} \text{ m}^2 = 0.0200 \text{ m}^2$.
Separation, $d = 0.40 \text{ cm} = 0.40 \times 10^{-2} \text{ m} = 0.0040 \text{ m}$.
Permittivity of free space, $\epsilon_0 = 8.85 \times 10^{-12} \text{ F/m}$.
Voltage, $V = 500 \text{ V}$.
Dielectric constant, $K = 2.60$.

(a) Compute its capacitance.

The capacitance is $\boxed{4.43 \times 10^{-11} \text{ F}}$ (or $44.3 \text{ pF}$).

(b) If the capacitor is connected across a 500 V source, find the charge on it, the energy stored in it, and the value of E between the plates.

The charge on the capacitor is $\boxed{2.21 \times 10^{-8} \text{ C}}$.

The energy stored in the capacitor is $\boxed{5.53 \times 10^{-6} \text{ J}}$.

The electric field between the plates is $\boxed{1.25 \times 10^5 \text{ V/m}}$.

(c) If a liquid with K = 2.60 is poured between the plates so as to fill the air gap, how much additional charge will flow onto the capacitor from the 500 V source?

The voltage source remains $V = 500 \text{ V}$.

The additional charge that will flow onto the capacitor is $\boxed{3.54 \times 10^{-8} \text{ C}}$.