Introduction to Circuits
BME253L - Fall 2025
Learning Objectives
- What are circuits?
- How does electric circuit analysis apply to other biomedical systems?
- Circuit analysis conventions
Circuit
Circuits are interconnection of elements (sources and loads).
What are common sources and loads in electronic circuits?
Sources
Voltage differentials -> EMF -> electric current (moving electrons) to flow through “closed circuit” paths.
The potential energy in the source to move electrons to the load, where that energy is either dissipated or stored.
Biomedical Circuit Correlates
Cardiovascular
- Source: Heart (pressure differential)
- Load:
- Circulatory system
- Organs
- Resistance & elasticity (storage of energy)
- Current: Volumetric Flow Rate
Cardiovascular Analogy
How does sympathetic and parasympathetic tone modulate systemic resistance and pressure?
Respiratory
- Source: Diaphragm & Intercostal Muscles
- Load: Airways / Lungs
- Current: Volumetric Airflow Rate
What is charge?
\[ \begin{gather} q_e = -1.602 \times 10^{-19} C (Coulomb)\\ q_p = -q_e \end{gather} \]
What is current?
Current
Current is the time rate change of charge passing through a defined area.
\[ i = \frac{dq}{dt} \left[\frac{C}{s}\right] = [A] (Ampere) \]
Polarity Conventions
- (+) direction of current flow represents flow of (+) charges (i.e., not electrons)
SI Units
Coulombs and amperes are SI units.
| Power of 10 | Prefix |
|---|---|
| \(\times 10^{12}\) | T (Tera) |
| \(\times 10^9\) | G (Giga) |
| \(\times 10^6\) | M (Mega) |
| \(\times 10^3\) | k (kilo) |
| \(\times 10^{-3}\) | m (milli) |
| \(\times 10^{-6}\) | \(\mu\) (micro) |
| \(\times 10^{-9}\) | n (nano) |
| \(\times 10^{-12}\) | p (pico) |
Common Current Magnitudes
| Description | Approx. Magnitude |
|---|---|
| Circuit breaker limits / house electrical wires max | 10-20 A |
| Home circuit breaker total | 200-300 A |
| Hairdryer | < 10 A |
| Car Battery Max | 100s A |
| Laptop Battery | < 1 A |
| Cellphone Battery | 10 mA (idle) 3 A (cell, camera) |
| Nerve Membrane Current | pA |
What is voltage?
A voltage differential represents the energy (\(dW\)) available in flowing charge (\(dq\)), avialalbe as stored potential energy in a source.
\[ V = \frac{dW}{dq} \left[\frac{J}{C}\right] = [V] (Volt) \]
Common Voltage Magnitudes
| Description | Approx. Magnitude |
|---|---|
| Wall Outlet | 110-240 V (AC) |
| Transmission Line | kV-MV |
| Lightning | ~100 MV |
| Alkaline Battery Cell | ~1.5 V |
| Nerve Action Potential | ~75 mV |
Voltage is a relative quantity; absolute voltage does not exist!
What is power?
Power represents the rate at which work can be done (i.e., energy / unit time).
\[ P = \frac{dw}{dt} = \frac{dW}{dq} \frac{dq}{dt} = VI \]
What do the units look like?
\[ \left[\frac{J}{C} \frac{C}{s}\right] = \left[\frac{J}{s}\right] = [W] (Watt) \]
What happens to power?
Circuit elements my absorb (dissipate or store) [load] or provide [source] power.
Sign Conventions
\(P < 0\): energy is provided to the circuit (source) \(P > 0\): energy is dissipated / stored (load)
Power dissipated by a circuit element (load) is (+) when (+) current (\(I\)) flows from a (+) -> (-) voltage (V).
