Answer:
20.60 kV
Explanation:
Capacitance of parallel plates without dielectric between them is:
[tex] C=\frac{\varepsilon_{0}A}{d}[/tex]
with d the distance between the plates, A the area of the plates and ε₀ the constant [tex] 8.85419\times10^{-12}\frac{C^{2}}{Nm^{2}}[/tex], so :
[tex]C_0=\frac{(8.85419\times10^{-12})(0.0029)}{0.0100\times10^{-3}}=2.57\times10^{-9} F [/tex]
But the dielectric constant is defined as:
[tex]k=\frac{C}{C_{0}} [/tex]
With C the effective capacitance (with the dielectric) and Co the original capacitance (without the dielectric). So, the new capacitance is:
[tex]C=kC_0 [/tex]
But capacitance is related with voltage by:
[tex]C=\frac{Q}{V} [/tex]
with Q the charge and V the voltage, using the new capacitance and solving for V:
[tex]kC_0=\frac{Q}{V} [/tex]
[tex] V=\frac{Q}{kC_0}=\frac{0.18\times10{-3}}{(3.4)(2.57\times10^{-9})}=20599.68V=20.60 kV[/tex]
20.6kV
The capacitance (C₀) of a parallel plate capacitor is given by;
C₀ = A x ε₀ / d
Where;
A = Area of one of the plates = 29cm² = 0.0029m²
ε₀ = permittivity of free space = 8.85 x 10⁻¹²F/m
d = distance between the plates = 0.0100mm = 0.00001m
But since there is a dielectric material (nylon) between the plates, the effective capacitance (C) will increase to k x C₀. i.e
C = k x C₀ -----------------------(i)
Where;
k = dielectric constant = 3.4 and;
C₀ = A x ε₀ / d
Substitute the value of C₀ into equation (i) to give;
C = k x A x ε₀ / d -----------------(ii)
Substitute the values of k, A, d and C₀ into equation (ii) to give;
C = 3.4 x 0.0029 x 8.85 x 10⁻¹² / 0.00001
C = 8.7261 x 10⁻⁹ F
From the capacitance (C) calculated above, the amount of voltage(V) supplied can be found using the following relation;
Q = C x V ------------------------------(iii)
Where Q is the charge on the capacitor = 0.18mC = 0.18 x 10⁻³C
Make V the subject of the formula in equation (iii) above;
V = Q / C
Substitute the values of Q and C into the equation to give;
V = (0.18 x 10⁻³) / (8.7261 x 10⁻⁹)
V = 0.0206 x 10⁶V
V = 20600V
V = 20.6kV
Therefore, the voltage applied in kV is 20.6
