Charge Ratios on Capacitors (Adapted from a TYC WS Project ranking task by D. Ta
ID: 1441072 • Letter: C
Question
Charge Ratios on Capacitors (Adapted from a TYC WS Project ranking task by D. Takahashi) Eight capacitor circuits are shown below. All of the capacitors are identical and all are fully charged. The batteries are also identical. In each circuit, one capacitor is labeled C1 and another labeled C 2. Rank these circuits in terms of the value of the ratio of the charge on C 1 to the charge on C 2. (If q1 is the charge on C 1, and q 2 is the charge on C 2, the value of the ratio is q 1/ q 2). Rank the circuit in which the value of the ratio is largest first, and rank the circuit in which the value of the ratio is the smallest last. If two or more circuits result in identical values for the ratio, give these circuits equal ranking. Express your ranking symbolically. (For example, suppose the ratio was highest for D and G and lowest for A and E with the in-between ratios being equal, then the symbolic ranking would be D = G > B = C = H = F > A = E [Beware: This is only a sample, not a correct answer!
CAT C2Explanation / Answer
A) q1=q2=CV/2
q1/q2=1
B) V1=V2=V
q1+q2=q=CeV=3CV/2
q1=CV/2
q2=CV
q1/q2=1/2
C) q1=q2=CV
q1/q2=1
D) Cs=C/2
q1=q2=CsV=CV/2
q1/q2=1
E) q=CeV=2CV/3
q1=q=2CV/3
q=CpV2=2CV2 --> V2=q/2C=V/3
q2=C2V2=CV/3
q1/q2=2
F) q=CeV=CV/3=q1=q2
Ce=C/3
q1=q2=CV/3
q1/q2=1
G) The same as E)
H) The same as F)
E=G>A=C=D=F=H>B
I hope I did not mistake the calculation...