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.

    (d) Assume C3 is increased. Explain what happens to the charge stored by each capacitor.
     Q3, Q1, and Q2 increases. Q3 and Q2 increases; Q1 decreases.       Q3 and Q1 increases; Q2 decreases. All charges stay the same.

Three capacitors are connected to a battery as shown in the figure below. Their capacitances are C1 = 3C, C2 = C, and C3 = 5C. What is the equivalent capacitance of this set of capacitors (in terms of C)? State the ranking of the capacitors according to the charge they store, from largest to smallest.

Explanation / Answer

a)

C2 and C3 are in parallel

C23=C2+C3 =C+5C

C23=6C

C1 and C23 are in series

Ceq =C1*C23/(C1+C23)

Ceq =3C*6C/(3C+6C)

Ceq =2C

b)

total charge

Q=Ceq*V =2C*V

Q=2CV

Q1=Q=2CV

Q2=Q*(C2/C2+C3) =2CV*(C/C+5C)

Q2=0.33CV

Q3 =Q-Q2=1.67CV

Q1>Q3>Q2

c)

V1 =Q1/C1 =2CV/3C

V1=0.67V

V2=Q2/C2 =0.33CV/C

V2=0.33V

V3=Q3/C3 =3.33CV/5C

V3=0.33V

V1>V2=V3

d)

Q1 increases and Q2 and Q3 decrease

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