Question

Consider the circuit pictured with 6 capacitors connected to a 20V emf.

A. What is the total effective capacitance of the 6 capacitors connected in the picture?

B. Calculate the amount of charge of the 1.5 uF capacitor.

Answer 1

1.5 Ceq2 Ceql 75 30.5 2.5 Ceq2

We use the equivalent capacitor equations

Serie   1/Ceq = 1/C1 + 1/C2+…

Parallel    Ceq = C1 + C2 + …

We use the diagram of the attached file

1/Ceq1 = 1/2 + 1/ 30.5      1/ Ceq1 = 30.5+2 ) / 30.5   2 = 32.5/61

Ceq1= 61/32.5 mF

Ceq2 = 75 + 1.5   

Ceq2= 76.5 mF

1/Ceq3= 1/2.5 + 1/ 76.5    1/Ceq3= 76.5+2.5)/ 76.5 2.5 =79/191.25

Ceq3 = 191.25/79   mF

Ceqtotal = Ceq1 + 6 + Ceq3      Ceqtotal = 61/32.5 + 6 + 191.25/ 79 = 10.29 mF

Ceqtotal = 10 mF

We calculus the charge in capacitors

Parallel    Q = Q1 +Q2 + …

Serie    Q = Q1 = Q2

Calculus the charge in Ceq3      All multiplied by 10^-6  

Qtotal = Ceqtotal V       Qtotal = 10 20 = 200 C

Qtotal = Q1 + Q6 + Q3

In the parallel circuit V = cte

Q1 = Ceq1 V     Q1 = 61/32.5    20 = 37.5 C

Q6= C6 V         Q6= 6 20 = 120 C

Q3= Ceq3 V      Q3 = 191.25/79 20 = 48.4 C

In a serie circuit

Q3 = Q2           

Q2 = Q75 + Q1.5          Q2 = 75 V2 + 1.5 V2        48.4 = (75+ 1.5 ) V2        V2= 48.4/76.5   V2= 0.63 V

Q1.5 = 1.5 0.63   = 0.945 10^-6 C