(a) The capacitance of a parallel-plate capacitor is given by the formula:
C = ε₀(A/d)
where C is the capacitance, ε₀ is the permittivity of free space (ε₀ = 8.85 x 10⁻¹² F/m), A is the area of the plates, and d is the separation between the plates.
Rearranging the formula, we can find the area A:
A = Cd/ε₀
Plugging in the given values:
C = 1.40 mF = 1.40 x 10⁻³ F
d = 2.00 µm = 2.00 x 10⁻⁶ m
ε₀ = 8.85 x 10⁻¹² F/m
A = (1.40 x 10⁻³ F)(2.00 x 10⁻⁶ m)/(8.85 x 10⁻¹² F/m)
= 3.16 x 10⁻⁷ m² (rounded to two significant figures)
Therefore, the area of the parallel plates must be 3.16 x 10⁻⁷ m².
(b) The maximum voltage that can be applied across a capacitor is given by the formula:
V = Q/C
where V is the voltage, Q is the charge stored in the capacitor, and C is the capacitance.
Rearranging the formula, we can find the maximum voltage V:
V = QC
The maximum charge that can be stored in the capacitor is given by:
Q = CV
Plugging in the given values:
C = 1.40 mF = 1.40 x 10⁻³ F
Q = (1.40 x 10⁻³ F)(V) = 1.40 x 10⁻³V
Now we can solve for V:
V = (1.40 x 10⁻³ F)(V)/(1.40 x 10⁻³ F)
= V
Therefore, the maximum voltage that can be applied is V.
(c) The maximum charge that can be stored in the capacitor is given by:
Q = CV
Plugging in the given values:
C = 1.40 mF = 1.40 x 10⁻³ F
V = V
Q = (1.40 x 10⁻³ F)(V)
= 1.40 x 10⁻³V
Therefore, the maximum charge that can be stored is 1.40 x 10⁻³V C.
(d) The volume of Teflon alone in the capacitor is given by:
V = Ad
where V is the volume, A is the area of the plates, and d is the separation between the plates.
Plugging in the given values:
A = 3.16 x 10⁻⁷ m²
d = 2.00 µm = 2.00 x 10⁻⁶ m
V = (3.16 x 10⁻⁷ m²)(2.00 x 10⁻⁶ m)
= 6.32 x 10⁻¹³ m³ (rounded to two significant figures)
Therefore, the volume of Teflon alone in the capacitor is 6.32 x 10⁻¹³ m³.
A large capacitance of 1.40 mF is needed for a certain application. (a) Calculate the area the parallel plates of such a capacitor must have if they are separated by 2.00 µm of Teflon. m2 (b) What is the maximum voltage that can be applied? V (c) Find the maximum charge that can be stored. C (d) Calculate the volume of Teflon alone in the capacitor. m3
1 answer