An electronics technician is repairing a power supply filter network. The circuit requires… — Armed Services Vocational Aptitude Battery (ASVAB)

An electronics technician is repairing a power supply filter network. The circuit requires replacing a section containing two $12\text{ }\mu\text{F}$ capacitors connected in series, which are arranged in parallel with a single $6\text{ }\mu\text{F}$ capacitor. What is the total equivalent capacitance of this entire combination?

A
$4.8\text{ }\mu\text{F}$
$12\text{ }\mu\text{F}$ Answer
C
$30\text{ }\mu\text{F}$
D
$12\text{ nF}$

Answer

The total equivalent capacitance of the network is

12\text{ }\mu\text{F}

To find the total equivalent capacitance, solve the series combination first: two

12\text{ }\mu\text{F}

capacitors in series provide an equivalent capacitance of

\frac{12 \times 12}{12 + 12} = 6\text{ }\mu\text{F}

. Next, add the parallel branch value directly:

6\text{ }\mu\text{F} + 6\text{ }\mu\text{F} = 12\text{ }\mu\text{F}

Step-by-Step Solution

Calculate the equivalent capacitance of the two series-connected capacitors.

C_{\text{series}} = 6\text{ }\mu\text{F}

Capacitors in series combine reciprocally using the formula

C_{\text{series}} = \frac{C_1 \times C_2}{C_1 + C_2} = \frac{12 \times 12}{12 + 12} = \frac{144}{24} = 6\text{ }\mu\text{F}

Add the equivalent series capacitance to the parallel capacitor.

C_{\text{total}} = 12\text{ }\mu\text{F}

Capacitors in parallel add directly together:

C_{\text{total}} = C_{\text{series}} + C_3 = 6\text{ }\mu\text{F} + 6\text{ }\mu\text{F} = 12\text{ }\mu\text{F}

Key Concept

Capacitors in series combine reciprocally (reducing total capacitance), whereas capacitors in parallel add directly together (increasing total capacitance).

Alternative Method

Since the two series capacitors are identical, their equivalent capacitance is simply half of one capacitor's value:

\frac{12\text{ }\mu\text{F}}{2} = 6\text{ }\mu\text{F}

. Adding the identical

6\text{ }\mu\text{F}

parallel branch doubles this value back to

12\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