An air condenser has an area of 100 cm^2 the plates being 4mm apart. It is connected in series with another condenser having plate area of 20cm^2 plates being separated by dielectric 0.1mm thick with E=2.5. If the potential difference across an condenser is 1000volts; find the potential difference across the combination.
Across which one?
q = V1C1
V2 = q/C2
Find C1 and C2 first.
To find the potential difference across the combination of the two capacitors connected in series, we first need to calculate the capacitance of each capacitor.
The capacitance of a parallel plate capacitor can be calculated using the formula:
C = (ε0 * εr * A) / d
Where:
C is the capacitance
ε0 is the permittivity of free space (8.85 x 10^-12 F/m)
εr is the relative permittivity of the dielectric material
A is the area of the plates
d is the separation between the plates
Let's calculate the capacitance of the first capacitor:
C1 = (ε0 * εr * A1) / d1
Given:
A1 = 100 cm^2 = 100 x 10^-4 m^2
d1 = 4 mm = 4 x 10^-3 m
Now, using the given information, the relative permittivity of free space (εr0) is 1, and the area (A1) and separation (d1) are known.
Substituting the values into the formula:
C1 = (8.85 x 10^-12 F/m * 1 * 100 x 10^-4 m^2) / 4 x 10^-3 m
= 2.213 x 10^-12 F
Now, let's calculate the capacitance of the second capacitor:
C2 = (ε0 * εr * A2) / d2
Given:
A2 = 20 cm^2 = 20 x 10^-4 m^2
d2 = 0.1 mm = 0.1 x 10^-3 m
εr = 2.5
Substituting the values into the formula:
C2 = (8.85 x 10^-12 F/m * 2.5 * 20 x 10^-4 m^2) / 0.1 x 10^-3 m
= 8.85 x 10^-11 F
Now that we have the capacitance of each capacitor, we can calculate the total capacitance (C_total) when capacitors are connected in series:
1/C_total = 1/C1 + 1/C2
Substituting the values:
1/C_total = 1/(2.213 x 10^-12 F) + 1/(8.85 x 10^-11 F)
= 4.521 x 10^10 F^-1
C_total = 1 / (4.521 x 10^10 F^-1)
= 2.208 x 10^-11 F
Finally, to find the potential difference across the combination of the two capacitors connected in series, we can use the formula:
V_total = V1 + V2
Given:
V1 = V2 = 1000 V (as they are in series)
V_total = 1000 V + 1000 V
= 2000 V
Therefore, the potential difference across the combination of the two capacitors connected in series is 2000 volts.