During the maintenance of an aerospace navigation system, an avionics technician isolates … — Armed Services Vocational Aptitude Battery (ASVAB)

During the maintenance of an aerospace navigation system, an avionics technician isolates a filtering network to verify its total capacitance. The network is configured as follows: a $20 \mu\text{F}$ capacitor and a $5 \mu\text{F}$ capacitor are wired in series. This series combination is placed in parallel across a $36 \mu\text{F}$ capacitor. Finally, this entire grouped section is wired in series with a $120 \mu\text{F}$ capacitor. What is the total equivalent capacitance of this filtering network? Enter your answer as a number.

Answer: 30 \mu\text{F}

Answer

To find the total equivalent capacitance, you must simplify the circuit step-by-step applying the specific rules for capacitors, which are the exact reverse of resistors. First, the

20 \mu\text{F}

and

5 \mu\text{F}

series capacitors are combined using the product-over-sum method to yield

4 \mu\text{F}

. Next, this

4 \mu\text{F}

equivalent is added directly to the

36 \mu\text{F}

parallel capacitor, resulting in

40 \mu\text{F}

for the entire parallel section. Finally, this

40 \mu\text{F}

equivalent block is in series with the final

120 \mu\text{F}

capacitor. Using the product-over-sum method once more (

\frac{40 \times 120}{160}

), the final total equivalent capacitance equals

30 \mu\text{F}

Step-by-Step Solution

Calculate the equivalent capacitance of the

20 \mu\text{F}

and

5 \mu\text{F}

series pair.

4 \mu\text{F}

Capacitors in series are calculated using the reciprocal formula or product-over-sum rule:

\frac{20 \times 5}{20 + 5} = 4

Calculate the equivalent capacitance of the parallel section.

40 \mu\text{F}

The

4 \mu\text{F}

series equivalent is in parallel with the

36 \mu\text{F}

capacitor. Capacitors in parallel simply add together:

4 + 36 = 40

Calculate the final total capacitance of the entire network.

30 \mu\text{F}

The

40 \mu\text{F}

equivalent section is in series with the

120 \mu\text{F}

capacitor. Using the product-over-sum rule again:

\frac{40 \times 120}{40 + 120} = 30

Key Concept

Calculating equivalent capacitance in compound series-parallel networks

Estimated Time:3m 0s

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