A circuit is constructed with five capacitors and a battery as shown. The values

Question

A circuit is constructed with five capacitors and a battery as shown. The values for the capacitors are: C1 = C5 = 3.6 F, C2 = 2.8 F, C3 = 6.5 F, and C4 = 2.8 F. The battery voltage is V = 12 V.

1)What is Cab, the equivalent capacitance between points a and b?

2)What is Cac, the equivalent capacitance between points a and c?

3)What is Q5, the charge on capacitor C5?

4)What is Q2, the charge on C2?

5)What is Q1, the charge on capacitor C1?

6)What is V4, the voltage across capacitor C4?

Please help with these questions.

A circuit is constructed with five capacitors and a battery as shown. The values for the capacitors are: C1 = C5 = 3.6 F, C2 = 2.8 F, C3 = 6.5 F, and C4 = 2.8 F. The battery voltage is V = 12 V. What is Cab, the equivalent capacitance between points a and b? What is Cac, the equivalent capacitance between points a and c? What is Q5, the charge on capacitor C5? What is Q2, the charge on C2? What is Q1, the charge on capacitor C1? What is V4, the voltage across capacitor C4?

Explanation / Answer

a)

C2 and C3 are in series

C23 =C2*C3/(C2+C3) =2.8*6.5/(2.8+6.5)

C23=1.957 uF

C23 and C4 are in parallel

Cab =C4+C23=2.8+1.957

Cab=4.757 uF

b)

Cac =Cab*C1/(Cab+C1) =3.6*4.757/(3.6+4.757)

Cac=2.05 uF

c)

equivalent capacitavne

Ceq =Cac*C5/(Cac+C5) =2.05*3.6/(2.05+3.6)

Ceq =1.3 uF

Q5=Q=Ceq*V =1.3*12

Q5=15.67 uC

d)

Q2 =Q*(C23/C23+C4)

Q2=15.67*(1.957/1.957+2.8)

Q2=6.45 uC

e)

Q1=Q=15.67 uC

f)

Charge on Q4=

Q4=Q-Q2 =15.67-6.45

Q4=9.22 uC

V4=Q4/C4 =9.22/2.8

V4=3.3 V

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