Please can someone help me with both of these. I keep getting a wrong number and
ID: 1327964 • Letter: P
Question
Please can someone help me with both of these. I keep getting a wrong number and cant find out why
A parallel-plate capacitor has capacitance Co = 2.00 pF when there is air between the plates. The separation between the plates is 1.80 (a) What is the maximum magnitude of chargeQ that can be placed on each plate if the electric field in the region between the plates is not to exceed 3.00 x 104 V/m? (b) A dielectric with K- 2.50 is inserted between the plates of the capacitor, completely filling the volume between the plates. V/m? Now what is the maximum magnitude of charge on each plate if the electric field between the plates is not to exceed 3.00 x 104Explanation / Answer
We know that the capacitence,c=q/v
E=30000 V/m
Seperation between the plates,d=1.8mm
So voltage needed to produce the electric filed intensity will be 1.8mm x 30000V/m = 54V.
A) So q=cv;
=2pFx54V
=108pC
B)So when we insert the dielectric, it will affect the capacitance of the capacitor; since it is directly proportional to capacitance
So the new capacitance will be 2.5x2pF=5pF.
Now it can store more charges...
q=5pFx75V
=375nC
2)
Energy stored in capacitor = U = 7.52 J
We know that the energy,U =(1/2)CV2
C =(eo)A/d
C*d=(eo)A=constant
C2d2=C1d1
C2=C1d1/d2
The separation between the plates is 3.45mm . The separation is decreased to 1.5 mm.
Initial separation between the plates =d1= 3.45mm .
Final separation = d2 = 1.50 mm
(A) if the capacitor was disconnected from the potential source before the separation of the plates was changed, charge 'q' remains same
Energy=U =(1/2)q2/C
U2C2 = U1C1
U2 =U1C1 /C2
U2 =U1d2/d1
Final energy = Uf = initial energy *d2/d1
Final energy = Uf =7.52 *1.50/3.45
(A) Final energy = Uf = 3.27J
B) If the capacitor remained connected to the potential source while the separation of the plates was changed, potential remains same.
Final energy = Uf =(1/2)CV2
Final energy = Uf =(1/2)[C1d1/d2]V2
Final energy = Uf =(1/2)[C1V2]d1/d2
Final energy = Uf = initial energy *d1/d2
Final energy = Uf =7.52 *3.45/1.50
Final energy = Uf =17.296 J