An electronics technician is assembling an energy-storage circuit for an industrial sensor… — Armed Services Vocational Aptitude Battery (ASVAB)

An electronics technician is assembling an energy-storage circuit for an industrial sensor module. The circuit consists of two $100\text{ }\mu\text{F}$ capacitors connected in series, and this entire combination is wired in parallel with a single $150\text{ }\mu\text{F}$ capacitor. What is the total equivalent capacitance of this circuit in microfarads ( $\mu\text{F}$ )?

Answer: 200 $\mu\text{F}$

Answer

The total equivalent capacitance of the circuit is

200\text{ }\mu\text{F}

For capacitors in series, total capacitance decreases and is calculated as

\frac{1}{C_{\text{series}}} = \frac{1}{100\text{ }\mu\text{F}} + \frac{1}{100\text{ }\mu\text{F}} = \frac{2}{100\text{ }\mu\text{F}}

, giving

C_{\text{series}} = 50\text{ }\mu\text{F}

. When this combination is connected in parallel with the

150\text{ }\mu\text{F}

capacitor, parallel capacitances add directly:

C_{\text{total}} = 50\text{ }\mu\text{F} + 150\text{ }\mu\text{F} = 200\text{ }\mu\text{F}

Step-by-Step Solution

Calculate the equivalent capacitance of the two

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

capacitors connected in series using the reciprocal formula

\frac{1}{C_{\text{series}}} = \frac{1}{C_1} + \frac{1}{C_2}

C_{\text{series}} = 50\text{ }\mu\text{F}

Capacitors in series combine inversely, meaning two identical capacitors in series have half the capacitance of one capacitor.

Add the capacitance of the parallel branch to the series equivalent:

C_{\text{total}} = C_{\text{series}} + C_3

C_{\text{total}} = 50\text{ }\mu\text{F} + 150\text{ }\mu\text{F} = 200\text{ }\mu\text{F}

Capacitors connected in parallel add directly because their effective plate areas combine, increasing overall charge storage capacity.

Key Concept

Series and parallel equivalent capacitance rules (series capacitors combine inversely; parallel capacitors add directly).

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic