Question

Consider the capacitor circuit shown to the right containing a 10 V battery, and 21 capacitors. Capacitors C to C20 are connected in series. The capacitance of each capacitor is given by: C21 10 V C20 C = C2 =... = C19 = C20 = 2 uf C21 = 3F (a) What is the equivalent capacitance of this circuit? Input your answer in microfarads.

Answer 1

Remember:

For parallel combination

Ceq = C1 + C2 + C3 +...............

for series combination

1/Ceq = 1/C1 + 1/C2 + 1/C3 + ............

for 2 capacitors in series it will be

Ceq = C1*C2/(C1+C2)

Using this Information:

Given that C1 to C20 are in series, So

1/Cs = 1/C1 + 1/C2 + 1/C3 + .......... + 1/C19 + 1/C20

Since C1 = C2 = C3 = ...... = C19 = C20 = 2 $\mu$ F, So

1/Cs = 1/2 + 1/2 + 1/2 + ...... 1/2 + 1/2 = 20/2 = 10

Cs = 1/10 = 0.1 $\mu$ F

Now Cs and C21 are in parallel, So

Ceq = Cs + C21

Ceq = 0.1 + 3

Ceq = equivalent capacitance = 3.1 $\mu$ F