Suppose in the figure ( Figure 1 ) that C 1 = C 2 = C 3 = 27.6 ? F and C 4 = 37.
ID: 3892025 • Letter: S
Question
Suppose in the figure(Figure 1) that C1=C2=C3=27.6?F and C4=37.2?F.
If the charge on C2 is Q2=55.4?C, determine the charge on each of the other capacitors.
q1,q3,q4
Determine the voltage across each capacitor.
v1,v2,v3,v4
Determine the voltage Vab across the entire combination.
In the circuit shown in the figure (Figure 1) , C1 = 3.6?F , C2 = 5.3?F , C3 = 3.8?F , and a voltage Vab = 15V is applied across points a and b. After C1 is fully charged the switch is thrown to the right.
What is the final charge on each capacitor?
q1,q2,q3
What is the final potential difference on each capacitor?
v1,v2,v3
Explanation / Answer
As C1 = C2,
so charge stored will be same, i.e. Q1 = Q2 = 55.4 microC
As the potential difference across C1-C2 & C3 are same, as well as the capaitance value of the three are same, so the charge stored on C3 will be double in order to maintain eqal potential difference.
So, Q3 = 55.4 x 2 = 110.8 microC.
Q4 = Q1 + Q3 = 166.2 microC.
V1 = Q1 x C1 = 55.4 x 10^-6 / ( 27.6 x 10^-9) (C1 = 27.6 nF)
= 2000 V.
V2 = 2000 V
V3 = 2000 + 2000 = 4000 V
V4 = 166.2 x 10^-6 / (37.2 x 10^-9)
= 4468 V.
Q1 = 15 x 3.6 x 10^-9 (C1 = 3.6 nF)
= 54 x 10^-9 C
= 54 nC.
C1 : (C2 + C3) = 3.6 : (5.3 + 3.8)
= 3.6 : 9.1
3.6y + 9.1y = 54
y = 4.25
Q1 final = 3.6y = 15.3 nC
Q2 + Q3 = 9.1y = 38.675 nC
C2:C3 = 5.3:3.8
5.3z + 3.8z = 38.675
z = 4.25
Q2 = 5.3z = 22.525 nC
Q3 = 3.8z = 16.15 nC.
V1 = V2 = V3 = Q1 /C1 = Q2/C2 = Q3/C3 = 4.25 V.