A charged capacitor will discharge slowly, even if it's terminal are 'open circuit' that is ,not connected to anything this occurs because the dielectric between the two plates of the capacitor acts as a very poor conductor, allowing a very small leakage current to flow between the two plates,thus discharging them
A capacitor consists of two plates of area 50cm^2 ,separated by a sheet of polythene 0.1mm thick.the capacitor is briefly connected to a power supply, producing a potential difference between the plates of 15v calculate
A.the capacitance of the capacitor
B.the electrical resistance of the
dielectric between the two plates
C.the initial leakage current through the
capacitor when it is disconnected from the power supply
A. The capacitance of the capacitor is given by C = εA/d, where ε is the permittivity of the dielectric, A is the area of the plates, and d is the distance between the plates. In this case, C = 8.85 x 10^-12 F.
B. The electrical resistance of the dielectric between the two plates is given by R = ρL/A, where ρ is the resistivity of the dielectric, L is the length of the dielectric, and A is the area of the plates. In this case, R = 1.78 x 10^14 Ω.
C. The initial leakage current through the capacitor when it is disconnected from the power supply is given by I = V/R, where V is the potential difference between the plates and R is the electrical resistance of the dielectric. In this case, I = 8.45 x 10^-15 A.
A. The capacitance of the capacitor can be calculated using the formula:
C = ε₀ × (A / d)
Where C is the capacitance, ε₀ is the permittivity of free space (8.85 × 10^-12 F/m), A is the area of the plates (50 cm² = 0.005 m²), and d is the distance between the plates (0.1 mm = 0.0001 m).
Plugging in the values, we get:
C = (8.85 × 10^-12 F/m) × (0.005 m² / 0.0001 m)
C ≈ 442.5 × 10^-12 F
C ≈ 4.425 × 10^-10 F
So, the capacitance of the capacitor is approximately 4.425 × 10^-10 F.
B. The electrical resistance of the dielectric (polythene) can be calculated using the formula:
R = ρ × (L / A)
Where R is the resistance, ρ is the resistivity of the dielectric material, L is the thickness of the dielectric (0.1 mm = 0.0001 m), and A is the area of the plates (50 cm² = 0.005 m²).
Since the dielectric is a poor conductor, we can assume a high resistivity value such as 10^14 Ωm for polythene.
Plugging in the values, we get:
R = (10^14 Ωm) × (0.0001 m / 0.005 m²)
R ≈ 2 × 10^9 Ω
So, the electrical resistance of the dielectric between the two plates is approximately 2 × 10^9 Ω.
C. The initial leakage current through the capacitor when it is disconnected from the power supply can be estimated using Ohm's Law:
I = V / R
Where I is the current, V is the potential difference between the plates (15 V), and R is the resistance of the dielectric (2 × 10^9 Ω).
Plugging in the values, we get:
I = 15 V / 2 × 10^9 Ω
I ≈ 7.5 × 10^-9 A
I ≈ 7.5 nA
So, the initial leakage current through the capacitor when it is disconnected from the power supply is approximately 7.5 nA.
To calculate the capacitance of the capacitor, we can use the formula:
C = (ε₀ * εᵣ * A) / d
where:
C = capacitance
ε₀ = permittivity of free space (8.85 x 10⁻¹² F/m)
εᵣ = relative permittivity of polythene (dielectric constant)
A = area of the plates (50 cm², convert to m² by dividing by 10⁴)
d = thickness of the polythene (0.1 mm, convert to m by dividing by 1000)
A. Calculating the capacitance:
C = (8.85 x 10⁻¹² F/m * εᵣ * 50 cm² / 10⁴) / (0.1 mm / 1000)
Now, we need the value of the relative permittivity of polythene, εᵣ. It is typically around 2.25 for polythene.
C = (8.85 x 10⁻¹² F/m * 2.25 * 50 cm² / 10⁴) / (0.1 mm / 1000)
Calculate the above expression to find the value of capacitance C in Farads.
B. To calculate the electrical resistance of the dielectric, we need the formula:
R = (ρ * d) / A
where:
R = resistance
ρ = resistivity of the dielectric (specific to polythene)
d = thickness of the polythene (0.1 mm, convert to m by dividing by 1000)
A = area of the plates (50 cm², convert to m² by dividing by 10⁴)
C. To calculate the initial leakage current through the capacitor when it is disconnected from the power supply, we need Ohm's Law:
I = V / R
where:
I = current
V = potential difference (given as 15 V)
R = resistance of the dielectric (calculated in part B)
Plug in the values and calculate the current I in Amperes.
Note: To calculate parts B and C, we require specific values for the resistivity of the polythene and the relative permittivity of the polythene.
To calculate the capacitance of the capacitor, you can use the formula:
C = (ε₀ * εᵣ * A) / d
Where:
C is the capacitance
ε₀ is the permittivity of free space (around 8.85 x 10⁻¹² F/m)
εᵣ is the relative permittivity or dielectric constant of the polythene (given)
A is the area of the plates in square meters (converted from cm²)
d is the distance between the plates in meters (converted from mm)
A. Calculate the capacitance of the capacitor:
Given:
Area (A) = 50 cm² = 0.005 m²
Distance (d) = 0.1 mm = 0.0001 m
Relative permittivity (εᵣ) of polythene = ? (not given)
You need to know the relative permittivity or dielectric constant of polythene to calculate the capacitance.
B. Calculate the electrical resistance of the dielectric between the two plates:
The electrical resistance of a dielectric cannot be directly calculated with the given information. It would require conductivity or resistivity values of the dielectric material, which are not provided.
C. Calculate the initial leakage current through the capacitor when it is disconnected from the power supply:
The leakage current can be calculated using Ohm's Law:
I = V / R
Where:
I is the current
V is the potential difference (15V, given)
R is the resistance of the dielectric (not given)
Without the resistance of the dielectric, the value of the initial leakage current cannot be calculated.