Parallel-plate capacitor is made of two square plates 25 cm on a side and 1.0 mmapart. The capacitor is connected to a 50.0-V battery. With the battery still connected, the plates are pulled apart to a separation of 2.00 mm. What are the energies stored inthe capacitor before and after the plates are pulled farther apart? Why does the energydecrease even though work is done in separating the plates.

6.9 x 10^-7 J  

3.5 x 10^-7 J

Explanation:

Identify the unknown:  

The energies stored in the capacitor before and after the plates are pulled farther apart  

List the Knowns:

Voltage of the battery: V = 50 V

Area of the plates: A = 0.25 x 0.25 = 0.0625 m^2

Original distance between the plates: d = 1 mm = 10^-3 m

New distance between the plates: d = 2 mm = 2 x 10^-3 m

Permittivity of free space: ∈o = 8.85 x 10^-12 C^2/Nm^2-

Set Up the Problem:  

Capacitance of a parallel-plate capacitor:  

C=∈o*A/d

Energy stored in a capacitor:  

U_c=(1/2)*V^2*C

Solve the Problem:  

Before the plates are pulled farther apart:  

C = 8.85 x 10^-12 x 0.0625/10^-3 = 5•53 x 10^-10 F  

U_c = (1/2) x (50)^2 x 5.53 x 10^-10= 6.9 x 10^-7 J  

After the plates are pulled farther apart:  

C = 8.85 x 10^-12 x 0.0625/2*10^-3 = 2•77 x 10^-10 F  

U_c = (1/2) x (50)^2 x 2•77 x 10^-10 = 3.5 x 10^-7 J  

The energy decrease because the capacitance decrease, so the stored charge decrease and transferred to the battery  

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

0.93xc=0.93x3x10^8m/s

2.54cm is 1 inch

360seconds i 1 hr