A capacitor consisting of two parallel plates of area A = 4.6 m2 and spacing d = 0.150 m is filled with two parallel slabs of dielectric material of equal thickness and with dielectric constants 1 = 2.20 and 2 = 5.50, respectively. What is the total capacitance?

To find the total capacitance of the capacitor, we need to consider the effect of the dielectric materials on the capacitance. The presence of dielectric material between the plates increases the capacitance.

The capacitance of a parallel-plate capacitor without any dielectric material can be calculated using the formula:

C0 = ε0 * (A / d)

Where:
C0 is the capacitance without dielectric material
ε0 is the vacuum permittivity (8.85 x 10^-12 F/m)
A is the area of the plates (4.6 m^2)
d is the spacing between the plates (0.150 m)

Using these values, we can calculate the value of C0.

C0 = (8.85 x 10^-12 F/m) * (4.6 m^2 / 0.150 m)

Now, let's calculate the capacitance with the first dielectric slab (dielectric constant 1 = 2.20). The presence of the dielectric material increases the capacitance, and the new capacitance can be calculated using the formula:

C1 = 2.20 * C0

Similarly, we can calculate the capacitance with the second dielectric slab (dielectric constant 2 = 5.50) using the formula:

C2 = 5.50 * C0

Finally, the total capacitance is the sum of C1 and C2:

C_total = C1 + C2

Now, you can substitute the value of C0 into these formulas and calculate C1, C2, and C_total.