---
title: "Capacitance and series equivalent"
subject: "Basic Electronics Engineering"
chapter: 1
key: "semester_2/basic_electronics_engineering:capacitance-series"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/capacitance-series
site: BCT Engineering
---

# Capacitance and series equivalent

Basic Electronics Engineering · Chapter 1: Basic Circuits Concepts

- Asked in: 2068 Bhadra, 1+3 marks
- Video: [Capacitors in Series and Parallel Explained!](https://www.youtube.com/watch?v=zaT4JorVUz0) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/capacitance-series
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-1

## Question

Define capacitance. Find the equivalent capacitance when two capacitors of capacitance C1 and C2 are connected in series.

## Short answer

Capacitance is the ratio of charge stored to voltage (C=Q/V), unit farad. For series, charge Q is equal on both capacitors, voltages add: 1/Ceq = 1/C1 + 1/C2, giving Ceq = (C1·C2)/(C1+C2), which is smaller than the smallest individual capacitor.

## Answer

**Capacitance:** the ability of a capacitor to store electric charge. It is the ratio of the charge stored on one plate to the potential difference between the plates: C = Q/V. Unit: farad (F), where 1 F = 1 coulomb per volt.

#### Series equivalent
```text
 o---| |---| |---o
     C1    C2
  <-V1->  <-V2->
  <------ V ----->
```

In series, the same charge Q is stored on each capacitor (the charge on the connecting plates is only induced). The total voltage is the sum of the voltages:

V = V1 + V2

V1 = Q/C1, V2 = Q/C2, and for the equivalent capacitor V = Q/Ceq. Substituting:

Q/Ceq = Q/C1 + Q/C2

**1/Ceq = 1/C1 + 1/C2**

Ceq = (C1 × C2)/(C1 + C2)

The equivalent capacitance is smaller than the smallest individual capacitor. Example: C1 = 6 µF, C2 = 3 µF gives Ceq = 18/9 = 2 µF.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Capacitance is defined as
   A. C = V/Q
   B. C = Q/V, in farads
   C. C = QV
   D. C = I/V
   Answer: B. C = Q/V; 1 F = 1 C per volt. (Key point: Definition)

2. In a series connection of capacitors, what is common?
   A. The voltage across each
   B. The same charge Q on each
   C. The capacitance
   D. The energy stored
   Answer: B. The same charge Q is stored on each capacitor; the voltages add. (Key point: Series charge)

3. What is the equivalent capacitance of two capacitors in series?
   A. C1 + C2
   B. (C1 × C2)/(C1 + C2)
   C. C1 − C2
   D. (C1 + C2)/(C1 × C2)
   Answer: B. 1/Ceq = 1/C1 + 1/C2, so Ceq = C1C2/(C1 + C2). (Key point: Equivalent formula)

4. C1 = 6 µF and C2 = 3 µF in series give
   A. 9 µF
   B. 2 µF
   C. 4.5 µF
   D. 18 µF
   Answer: B. Ceq = 18/9 = 2 µF, smaller than the smaller capacitor. (Key point: Example)

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