Question

series-connected 10-pf and 60-pf capacitors are placed in parallel with series-connected 30-pf and 55-pf capacitors. determine the equivalent capacitance. the equivalent capacitance is pf.

Answer 1

To find the equivalent capacitance of the network, calculate the equivalent capacitance of each series-connected pair and then sum the results, as they are connected in parallel. The final equivalent capacitance is 28.35 pF.

Step-by-step explanation:

Calculating Equivalent Capacitance

When calculating the equivalent capacitance of a network of capacitors that includes series and parallel connections, we need to consider each configuration separately. For capacitors in series, the reciprocal of the equivalent capacitance (Ceq) is the sum of the reciprocals of the individual capacitances. For capacitors in parallel, the equivalent capacitance is simply the sum of their capacitances.

To find the equivalent capacitance of the given network, first calculate the equivalent capacitance of the series-connected 10-pF and 60-pF capacitors:

1 / Ceq,series1 = (1 / 10 pF) + (1 / 60 pF)

Ceq,series1 = 1 / [(1/10) + (1/60)] pF = 8.57 pF

Then calculate the equivalent capacitance of the series-connected 30-pF and 55-pF capacitors:

1 / Ceq,series2 = (1 / 30 pF) + (1 / 55 pF)

Ceq,series2 = 1 / [(1/30) + (1/55)] pF = 19.78 pF

Since these two series combinations are parallel to each other, their equivalent capacitances can be added directly:

Ceq,parallel = Ceq,series1 + Ceq,series2

Ceq,parallel = 8.57 pF + 19.78 pF

Ceq,parallel = 28.35 pF

The equivalent capacitance of the entire network is 28.35 pF.