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)?

Ceq

=    

(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.

?V1 = ?V2 < ?V3

?V1 > ?V2 = ?V3   

  ?V1 > ?V2 > ?V3

?V2 > ?V3 > ?V1

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

C1 = 3C, C2 = C, and C3 = 5C. (a) What is the equivalent capacitance of this set of capacitors (in terms of C)? Ceq = (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. ?V1 = ?V2 ?V2 = ?V3 ?V1 > ?V2 > ?V3 ?V2 > ?V3 > ?V1 (d) Assume C3 is increased. Explain what happens to the charge stored by each capacitor.

Explanation / Answer

remember these about Combination of capacitors

if C1 and C2 are the individual capacitor that re connected in series,

then their resultant capaciatnce 1/Cnet = 1/C1+1/C2 or Cnet   = C1C2/(C1+C2)

if c1 and C2 are connected in parallel, then their effective capacitancen is Cnet = C1+C2

also in sereis combination same amount of charge passes through each of the capacitiors

and in parallel combination, same PD (voltage) exists across each of the capacitor

so ehre

C2 and C3 are in parallel, net of these = (c2+C3)

Cnet = C+ 5C = 6C

so

this 6C is in series with C1 ( or 3C)

so

Cnet    = 3C * 6C/(3c+6C)

Cnet= Ceq = 2C
------------------------------

part B:

as chareg Q = CV

Cnet in parallel will be more and Cnet in series will be less

Q in parallel will b more than Q in series

so

Q1 > Q2 = Q3

------------------------

V1 = V2 < V3

-----------------------------------

d. is C3 is increased, Cnet of C2 and C3 increases,

Q increases but Q2 = Q3 will holds good

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