Module 3/5 · Weeks 7–9 · 30 h

AC, RC and RL circuits

DRT 113 Fundamentals of Electrical and Electronics

About 85 minDraft, awaiting reviewLast updated 26 September 2026

By the end of this module you will be able to

Explain sinusoidal AC, peak value, RMS value, frequency and period
Calculate charge, energy and the time constant of an RC circuit
Explain an RC low-pass filter and calculate its cut-off frequency
Explain induced voltage in an inductor and why voltage spikes occur in motor drive circuits
Explain the roles of capacitors and inductors in a drone's electrical system

Prerequisites: DRT 113 Modules 1–2 and DRT 111 Module 2 (trigonometric functions)

Electricity that changes with time

In Modules 1–2, voltage and current were constant. On a real drone, signals change all the time: ESCs switch motor current tens of thousands of times a second, chargers take AC mains, and sensors pick up high-frequency noise. Two components respond to these changes: the capacitor and the inductor. This module covers AC and these two components.

Alternating current

Alternating current (AC) changes direction and size back and forth as a sine wave:

v (t) = V_{p} sin (2 π f t)

where $V_{p}$ is the peak value and $f$ the frequency in hertz (cycles per second). The period is the time for one cycle, $T = 1/ f$ .

Figure 1. Sinusoidal AC: peak, RMS and period

Because the value keeps changing, we state its size as the RMS value: the DC value that would produce the same heating in a resistor. For a sine wave

V_{rms} = \frac{V _{p}}{2}

Example 1. Thai mains

Thailand’s low-voltage supply is specified at 230 V, 50 Hz (often called 220 V). The 230 V is the RMS value.

Peak $V_{p} = 230 \times 2 \approx 325$ V
Period $T = 1/50 = 0.02$ s, or 20 ms

Equipment on mains must therefore withstand a peak well above the label value. Mains is lethal: never open a charger or power supply while it is plugged in.

Capacitors

A capacitor stores charge on two conducting plates separated by an insulator. The charge is proportional to voltage:

Q = C V E = \frac{1}{2} C V^{2}

where $C$ is capacitance in farads (F); practical values are usually microfarads (µF) or nanofarads (nF).

Example 2. A capacitor at the ESC power input

A 1000 µF capacitor at 25 V:

Charge $Q = 0.001 \times 25 = 0.025$ C
Energy $E = \frac{1}{2} (0.001) (2 5^{2}) \approx 0.31$ J

That is tiny compared with the battery, but it can be released very fast. It supplies brief current bursts when the ESC switches and absorbs voltage spikes caused by long leads, which is why many ESC makers recommend a low-ESR capacitor close to the power terminals.

RC circuits and the time constant

When a capacitor is connected to a supply through a resistor, its voltage does not jump instantly; it rises exponentially:

v_{C} (t) = V (1 - e^{- t / R C}), τ = R C

Capacitor voltage while charging rises quickly then levels towards V; at time tau it reaches 63 percent — Figure 2. Capacitor voltage in an RC circuit while charging

$τ$ is the time constant. After $1 τ$ the voltage reaches about 63% of its final value; after $5 τ$ it is over 99%, and in practice considered fully charged.

The low-pass filter

A capacitor passes high frequencies more easily than low ones. Its frequency-dependent opposition, reactance $X_{C} = 1/ (2 π f C)$ , falls as frequency rises. A resistor in series with the output taken across the capacitor makes a low-pass filter with cut-off frequency

f_{c} = \frac{1}{2 π R C}

Example 3. Filtering sensor noise

With $R = 1$ kΩ and $C = 100$ nF:

f_{c} = \frac{1}{2 π ( 1000 ) ( 100 \times 1 0 ^{- 9} )} \approx 1.6 kHz

Signals much slower than this, such as slowly changing battery voltage, pass almost unchanged, while ESC switching noise at tens of kilohertz is strongly reduced.

Inductors

An inductor is a coil of wire. When its current changes, the magnetic field in the coil changes and induces a voltage that opposes the change:

v = L \frac{d i}{d t}

where $L$ is inductance in henries (H). An inductor behaves like “inertia” for current: it resists sudden change. Its reactance $X_{L} = 2 π f L$ rises with frequency, the opposite of a capacitor.

Example 4. Why voltage spikes happen

A motor winding or long lead has about 50 µH of inductance. If the ESC cuts 10 A in 1 µs:

v = 50 \times 1 0^{- 6} \times \frac{10}{1 \times 1 0 ^{- 6}} = 500 V

This brief spike is many times the battery voltage and can destroy MOSFETs. Real ESCs include diodes and capacitors to absorb the energy, and battery-to-ESC leads should be kept as short as possible.

On a drone, inductors appear in BLDC motor windings, switching regulators (such as buck BECs) and video-system noise filters.

Module lab

In class

View a function-generator signal on an oscilloscope. Read peak, period and frequency, and compare with the RMS value on a multimeter.
Build an RC circuit with $R = 10$ kΩ and $C = 100$ µF. Apply a slow square wave, measure the time to reach 63% and compare with $τ = 1$ s.
Feed sine waves of different frequencies into an RC filter, record output amplitude and find where it drops to about 70.7%.

Safety. Electrolytic capacitors are polarised and can burst if reversed; use a voltage rating above the working voltage.

Common mistakes

Watch out

Confusing peak with RMS. 230 V mains peaks at about 325 V.
Forgetting to convert µF and nF before calculating.
Reversing an electrolytic capacitor or using too low a voltage rating.
Ignoring the inductance of long leads, which causes spikes when current changes fast.

Summary

Sinusoidal AC is described by peak, RMS ( $V_{p} / 2$ ), frequency and period; Thai mains is 230 V, 50 Hz.
A capacitor stores $Q = C V$ and energy $\frac{1}{2} C V^{2}$ ; an RC circuit has time constant $τ = R C$ and filters at $f_{c} = 1/ (2 π R C)$ .
An inductor, $v = L d i / d t$ , resists changes in current and causes spikes when current is cut quickly.
On drones, capacitors steady the ESC supply and filter noise; inductors are in motors and power converters.

Check your understanding

What is the RMS value of a sine wave with a 17 V peak?
What is the period of a 400 Hz signal in milliseconds?
What is the time constant of an RC circuit with $R = 4.7$ kΩ and $C = 220$ µF?
For a low-pass cut-off near 160 Hz with $C = 1$ µF, what $R$ is needed?
If frequency doubles, how does an inductor’s reactance change?

Answers

$17/ 2 \approx 12$ V
$1/400 = 0.0025$ s, or 2.5 ms
$4700 \times 220 \times 1 0^{- 6} \approx 1.03$ s
$R = 1/ (2 π \times 160 \times 1 0^{- 6}) \approx 995 Ω$ , so about 1 kΩ
It doubles, since $X_{L} = 2 π f L$

Key formulas

Sinusoidal voltage	$v (t) = V_{p} sin (2 π f t)$
RMS value	$V_{rms} = \frac{V _{p}}{2}$
Period	$T = \frac{1}{f}$
Capacitor	$Q = C V, E = \frac{1}{2} C V^{2}$
RC charging	$v_{C} (t) = V (1 - e^{- t / R C}), τ = R C$
RC cut-off frequency	$f_{c} = \frac{1}{2 π R C}$
Inductor	$v = L \frac{d i}{d t}$
Reactance	$X_{C} = \frac{1}{2 π f C}, X_{L} = 2 π f L$

Key references

Ling, S. J., Sanny, J., & Moebs, W. (2016). University physics volume 2. OpenStax. link
Boylestad, R. L., & Nashelsky, L. (2013). Electronic devices and circuit theory (11th ed.). Pearson.
Horowitz, P., & Hill, W. (2015). The art of electronics (3rd ed.). Cambridge University Press.

In class / field

Lab or field practice from worksheets with a safety checklist

Learning evidence: Checked worksheets and quiz results

Module quiz

This is a formative self-check, not a graded exam

Knowledge domain: Electrical, electronics and power systems

AC, RC and RL circuits

By the end of this module you will be able to

Electricity that changes with time

Alternating current

Capacitors

RC circuits and the time constant

The low-pass filter

Inductors

Module lab

Common mistakes

Summary

Check your understanding

Key formulas

Key references

Further reading

DC and AC electrical circuits

In class / field

Module quiz

AC, RC and RL circuits

Lesson

By the end of this module you will be able to

Electricity that changes with time

Alternating current

Capacitors

RC circuits and the time constant

The low-pass filter

Inductors

Module lab

Common mistakes

Summary

Check your understanding

Key formulas

Key references

Further reading

DC and AC electrical circuits

In class / field

Module quiz