Three capacitors are connected to a battery as shown in the figure below. Their

Question

Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C.

(a) What is the equivalent capacitance of this set of capacitors (in terms of C)?


(b) State the ranking of the capacitors according to the charge they store, from largest to smallest.
Q  > Q  > Q  

(c) Rank the capacitors according to the potential differences across them, from largest to smallest.

?V2 > ?V3 > ?V1?V1 > ?V2 > ?V3    ?V1 = ?V2 < ?V3?V1 > ?V2 = ?V3

(d) Assume C3 is increased. Explain what happens to the charge stored by each capacitor.

Q3 and Q2 increases; Q1 decreases.All charges stay the same.    Q3, Q1, and Q2 increases.Q3 and Q1 increases; Q2 decreases.

Explanation / Answer

a,) for parallel setting, equivalent capacitance= C2 *C3 = 1*5 C = 5 C = C2"

( as C2 and C3 are in parallel )

Now C1 and C2" are in series:

for series, equivalent capacitance = (C1 *C2" )/ C1 +C2" = 1.875C

hence total equivalent capacitance is 1.875 C

b.) Q=CV

Now, potential difference accross C2 and C3 are same, therefore, capacitor with higher capacitace will have higher charge hence, Q2<Q3

Now capacitor in series have same charge,but different potential difference.

Hence, Q1 and Q2" (parallel equivalent of C2 and C3)are same.

Since parallel connections have same potential diff across them, hence,

Q3/C3 = Q2"/C2" (equivalent charge)

=> Q3 * C2"/C3 = Q2"

now C2"/C3 = 1

Hence Q1=Q2"=Q3>Q2

hence Q1=Q3>Q2

c.)   ?V2 = ?V3 as they are a parallel connection.

and Q1=Q2" .
=>V inversely proportional to C from Q=CV

Since C1=3C > C2" = 5C hence  ?V1 < ?V2 =?V3 =?V2" (equivalent ?V).

d.) If C3 is increased, then

equivalent C2" increases.

so in equivalent circuit , since V inversely proportional to C from Q=CV ; as C2" increases, ?V2" (equivalent  ?V across 2 and 3) decreases. Hence Q2 will decrease, Q1 increases as

Q1 * ( 1/C1 +1/ C2") = constant , from Kirchoffs law

now , Q1= Q2" .

Since, Q2" increases, and Q2 decreases and from Q1=Q2 + Q3, then Q3 must increase.

Hence Q1 and Q3 increases while Q2 decreases.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.