Consider three capacitors C 1 , C 2 , and C 3 and a battery. If only C 1 is conn
ID: 1401084 • Letter: C
Question
Consider three capacitors C1, C2, and C3 and a battery. If only C1 is connected to the battery, the charge on C1 is 30.0 µC. Now C1 is disconnected, discharged, and connected in series with C2. When the series combination of C2 and C1 is connected across the battery, the charge on C1 is 22.1 µC. The circuit is disconnected, and both capacitors are discharged. Next, C3,C1, and the battery are connected in series, resulting in a charge on C1 of 25.1 µC. If, after being disconnected and discharged, C1, C2, and C3 are connected in series with one another and with the battery, what is the charge on C1?
_____ µC
Explanation / Answer
for only C1 case:
Q = CV
30 = C1 * V
E = V = 30 / C1 this is the emf of the battery.
for c1 and c2 :
in series connection charge will be same on both capacitors
so Q = CV
22.1 = C1 * V1
22.1 = C2* V2
and V1 + V2 = v
22.1/c1 + 22.1/c2 = 30/c1
7.9/c1 = 22.1/c2
c2 = 2.80c1 ...(i)
for c1 and c3 :
in series connection charge will be same on both capacitors
so Q = CV
25.1 = C1 * V4
25.1 = C3* V5
v4 + V5 = V
25.1/c1 + 25.1/c3 = 30/c1
4.9/c1 = 25.1/c3
c3 = 5.13c1
for C1 , C2 and C3:
V' + V'' + V''' = V
Q / c1 + Q/c2 + Q/c3 = 30/c1
Q/c1 + Q/2.80c1 + Q/5.13c1 = 30/c1
Q ( 1 + 1/2.80 + 1/5.13) = 30
Q = 19.33 uC