please help me!
There is a capacitor C1 constructed by a pair of paralleled conductive plates 20 mm by 50 mm, spacing distance of 10 mm, and a ceramic dielectric with a relative permittivity of εr = 7500 (the absolute dielectric constant of vacuum or air ε0 = 8.85 ⨯ 10-12 F/m). Calculate the following:
a) Capacitance of this capacitance C1.
b)Construct another capacitor C2 with all the same conditions as C1 except the Doubled plate spacing distance. Calculate the total capacitance of these two capacitors C1 and C2 in Parallel.
c) Calculate the total capacitance of these two capacitors C1 and C2 in Series.
To calculate the capacitance of the given capacitor (C1), we can use the formula for the capacitance of parallel plate capacitors:
C = (ε0 * εr * A) / d
where C is the capacitance, ε0 is the absolute dielectric constant of vacuum or air (8.85⨯10^-12 F/m), εr is the relative permittivity of the ceramic dielectric (7500 in this case), A is the area of the plates (20 mm by 50 mm = 1000 mm^2 = 0.001 m^2), and d is the spacing distance between the plates (10 mm = 0.01 m).
a) Substituting the given values into the formula, we can calculate the capacitance (C1):
C1 = (8.85⨯10^-12 F/m * 7500 * 0.001 m^2) / 0.01 m
= (0.066375 F) / 0.01 m
= 6.6375 F
Therefore, the capacitance of capacitor C1 is 6.6375 Farads.
b) To calculate the total capacitance when capacitors C1 and C2 are connected in parallel, we can use the formula:
C_total = C1 + C2
Since capacitor C2 has the same conditions as C1 except for the doubled plate spacing distance, the only difference is in the value of d (20 mm = 0.02 m).
Using the formula from part a, we can calculate the capacitance of capacitor C2:
C2 = (8.85⨯10^-12 F/m * 7500 * 0.001 m^2) / 0.02 m
= (0.066375 F) / 0.02 m
= 3.31875 F
Therefore, the capacitance of capacitor C2 is 3.31875 Farads.
Now, we can calculate the total capacitance when C1 and C2 are connected in parallel:
C_total = C1 + C2
= 6.6375 F + 3.31875 F
= 9.95625 F
Therefore, the total capacitance of capacitors C1 and C2 in parallel is 9.95625 Farads.
c) To calculate the total capacitance when capacitors C1 and C2 are connected in series, we can use the formula:
1/C_total = 1/C1 + 1/C2
Using the values from parts a and b, we have:
1/C_total = 1/6.6375 F + 1/3.31875 F
Simplifying this equation:
1/C_total = 0.15092 + 0.301826
1/C_total = 0.452746
Now, we can find the reciprocal of both sides to solve for C_total:
C_total = 1 / 0.452746
= 2.20987 F
Therefore, the total capacitance of capacitors C1 and C2 in series is 2.20987 Farads.