Introduction to Circuits

BME253L - Fall 2025

Dr. Mark Palmeri, M.D., Ph.D.

Duke University

August 25, 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).

Question

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

Question

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.

Common Unit Prefixes
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

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

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

Important

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).