Kindly, show clear steps and pay attention to the units. Two parallel plates, ea
ID: 1425243 • Letter: K
Question
Kindly, show clear steps and pay attention to the units.
Two parallel plates, each having area A = 3494 cm2are connected to the terminals of a battery of voltage Vb = 6 V as shown. The plates are separated by a distance d = 0.53 cm.
1) What is Q, the charge on the top plate?
C
2) What is U, the energy stored in the this capacitor?
J
3) The battery is now disconnected from the plates and the separation of the plates is doubled ( = 1.06 cm). What is the energy stored in this new capacitor?
J
4) What is E, the magnitude of the electric field in the region between the plates?
N/C
5) Compare V, the magnitude of the new potential difference across the plates, to Vb, the voltage of the battery.
V < Vb
V = Vb
V > Vb
6)
Two uncharged parallel plates are now connected to the initial pair of plates as shown. How will the electric field, E, and potential difference across the plates, V, change, if at all?
A) Both E and V will remain the same
B) E will decrease and V will increase
C) E will increase and V will decrease
D) Both E and V will decrease
E) Both E and V will increase
Explanation / Answer
1) C = A/d = 3494*10-4 * 8.85*10-12 / 0.53*10-2 = 8.25*10-11 F
Q = CV = 8.25*10-11 *6 = 4.95*10-10 C
2) U = (1/2) CV2 = 1.485*10-9 J
3) When battery is disconnected, Charge on plates reamins conserved,
Since C = A/d so if d is doubled, C gets halved ,C = 4.12*10-11 F
U = (1/2) Q2/C = (1/2)*(4.95*10-10)2/4.12*10-11 = 2.97*10-9 J
4) new potential difference V = Q/Cnew = 2*Vb (since Q is same and C gets halved)
V = 12 V
E = V/d = 12/1.06*10-2 = 1132.075 N/C
5) V= 12 V, Vb = 6 V
So, V>Vb
6) In new configuration, Area has doubled, So C gets doubled, Q reamins conserved, So V will decrease.
Also distance between plates is same, So E will also decrease.
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