An air filled parallel plate capacitor has plates of area 0.0406 m^2 and seperation of 2.5*10^-6 m.
a)What is the capacitence for the setup?
b)Our capacitor is connected to a 550 v battery, how much energy is stored in the capacitor?
c) If -1 mJ of work is performed by the capapcitor's plates but it is never disconnected from the 550 V battery, what is the new seperation of the plates?
To answer these questions, we can use the formula for the capacitance of a parallel plate capacitor:
C = ε₀ * A / d
where:
C is the capacitance,
ε₀ is the permittivity of free space (8.85 x 10^-12 F/m),
A is the area of the plates, and
d is the separation between the plates.
a) To find the capacitance, we can substitute the given values into the formula:
C = (8.85 x 10^-12 F/m) * (0.0406 m^2) / (2.5 x 10^-6 m)
Solving this equation will give you the value of C in farads (F).
b) To calculate the energy stored in the capacitor, we can use the formula:
E = (1/2) * C * V^2
where E is the energy stored, C is the capacitance, and V is the voltage across the capacitor.
Substituting the given values:
E = (1/2) * C * (550 V)^2
Solving this equation will give you the value of E in joules (J).
c) To find the new separation of the plates, we need to use the work-energy principle. The work performed by the capacitor's plates is equal to the change in stored energy:
Work = ΔE = E_final - E_initial
Since the capacitor is never disconnected from the 550 V battery, the initial energy is given as:
E_initial = (1/2) * C_initial * (550 V)^2
Given that -1 mJ of work is performed:
ΔE = -1 x 10^-3 J
We can then calculate the final energy:
E_final = E_initial + ΔE
Now, we can rearrange the energy formula to solve for the new capacitance:
E_final = (1/2) * C_new * (550 V)^2
Then, solve for C_new:
C_new = 2 * E_final / (550 V)^2
Lastly, we can use the formula for capacitance to calculate the new separation:
C_new = ε₀ * A / d_new
Rearranging this formula gives us:
d_new = ε₀ * A / C_new
Substituting the given values, you can calculate the new separation, d_new, in meters (m).