An avionics communication filter assembly contains a capacitor network designed for signal… — Armed Services Vocational Aptitude Battery (ASVAB)

An avionics communication filter assembly contains a capacitor network designed for signal conditioning. The network consists of two $40\text{ }\mu\text{F}$ capacitors connected in series. This series combination is connected in parallel with an $80\text{ }\mu\text{F}$ capacitor. Finally, this entire parallel arrangement is connected in series with a single $25\text{ }\mu\text{F}$ capacitor. What is the total equivalent capacitance of the network, in microfarads ( $\mu\text{F}$ )?

Answer: 20 μF

Answer

The total equivalent capacitance of the network is

20\text{ }\mu\text{F}

The correct equivalent capacitance is

20\text{ }\mu\text{F}

. In capacitor networks, series components combine reciprocally (

\frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2}

) and parallel components add directly (

C_p = C_1 + C_2

). Resolving the initial series branch yields

20\text{ }\mu\text{F}

, which in parallel with

80\text{ }\mu\text{F}

produces

100\text{ }\mu\text{F}

. Finally, combining

100\text{ }\mu\text{F}

in series with

25\text{ }\mu\text{F}

results in

\frac{100 \times 25}{100 + 25} = 20\text{ }\mu\text{F}

Step-by-Step Solution

Calculate the equivalent capacitance of the initial series branch consisting of two

40\text{ }\mu\text{F}

capacitors.

C_{s1} = 20\text{ }\mu\text{F}

Capacitors in series combine reciprocally:

\frac{1}{C_{s1}} = \frac{1}{40\text{ }\mu\text{F}} + \frac{1}{40\text{ }\mu\text{F}} = \frac{2}{40\text{ }\mu\text{F}} = \frac{1}{20\text{ }\mu\text{F}}

Calculate the equivalent capacitance of the parallel combination formed by

C_{s1}

and the

80\text{ }\mu\text{F}

capacitor.

C_p = 100\text{ }\mu\text{F}

Capacitors in parallel add directly:

C_p = C_{s1} + C_3 = 20\text{ }\mu\text{F} + 80\text{ }\mu\text{F} = 100\text{ }\mu\text{F}

Calculate the total circuit capacitance by placing the parallel equivalent

C_p

in series with the

25\text{ }\mu\text{F}

capacitor.

C_{\text{total}} = 20\text{ }\mu\text{F}

Applying the series formula for the final combination:

\frac{1}{C_{\text{total}}} = \frac{1}{C_p} + \frac{1}{C_4} = \frac{1}{100\text{ }\mu\text{F}} + \frac{1}{25\text{ }\mu\text{F}} = \frac{1+4}{100\text{ }\mu\text{F}} = \frac{5}{100\text{ }\mu\text{F}} = \frac{1}{20\text{ }\mu\text{F}}

Key Concept

Calculation of total equivalent capacitance in compound series-parallel networks using reciprocal series addition and direct parallel addition rules.

Alternative Method

Use the product-over-sum shortcut for each two-component series reduction:

C_{s1} = \frac{40 \times 40}{40 + 40} = \frac{1600}{80} = 20\text{ }\mu\text{F}

. Next, add the parallel component directly:

C_p = 20 + 80 = 100\text{ }\mu\text{F}

. Finally, apply product-over-sum for the last series stage:

C_{\text{total}} = \frac{100 \times 25}{100 + 25} = \frac{2500}{125} = 20\text{ }\mu\text{F}

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Topics

More questions from this topic