The diagram above shows a circuit composed of an ideal battery, ideal wires, and
ID: 1259364 • Letter: T
Question
The diagram above shows a circuit composed of an ideal battery, ideal wires, and six capacitors. The battery provides a constant voltage of 9 volts. The capacitances of the six capacitors are given below.
C1= 14 nF , C2= 8 nF , C3= 16 nF , C4= 3 nF , C5= 6 nF , C6= 6 nF
a/ Find the voltage accross C4
b/ find the charge on C3
The diagram above shows a circuit composed of an ideal battery, ideal wires, and six capacitors. The battery provides a constant voltage of 9 volts. The capacitances of the six capacitors are given below. C1= 14 nF , C2= 8 nF , C3= 16 nF , C4= 3 nF , C5= 6 nF , C6= 6 nF Find the voltage accross C4 find the charge on C3Explanation / Answer
Part A)
First C2 and C3 are in parallel
C of that section = 24 nF
That is in series with C6, so in that leg...
1/C = 1/24 + 1/6
C = 4.8 nF
C1 and C5 are in series, so in that leg...
1/C = 1/14 + 1/6
C = 4.2 nF
The 4.2 and the 4.8 are in parallel
The C of the large parallel section is 9.0 nF
That is in series with C4, so
1/C = 1/3 + 1/9
C = 2.25 nF
Now we can find net Q
Q = CV = (2.25 X 10-9)(9) = 2.025 X 10-8 C
Then for the voltage on C4
Q = CV
(2.025 X 10-8) = (3 X 10-9)(V)
V = 6.75 Volts
Part B)
The voltage over the large parallel portion will be 9 - 6.75 = 2.25 Volts
The charge in the right side portion of that is...
Q = CV
Q = (4.8 X 10-9)(2.25)
Q = 1.08 X 10-8 Coulombs
Use that to find the V in the upper parallel section
Q = CV
(1.08 X 10-8) = (24 X 10-9)(V)
V = .45 Volts
Then finally for C3
Q = CV
Q = (16 X 10-9)(.45)
Q = 7.2 X 10-9 Coluombs (That is 7.2 nC)