Neuroscience: Membrane Potential, RC Circuit Model, and Time Constants

Membrane Potential

Difference in electric charge across the neuronal membrane.

Resting membrane potential

Typically ~ -70 mV in neurons.

RC circuit

A neuron can be represented as an RC circuit.

Resistance (R)

Due to membrane + channels.

Capacitance (C)

Due to lipid bilayer.

Battery

Provides a voltage (potential energy source) created by ion gradients (e.g., Na⁺, K⁺).

Capacitor

Stores electrical charge; cell membrane = capacitor.

Capacitance formula

ε = permittivity, A = area, d = thickness.

Resistor

Limits current flow; membrane proteins/channels = resistors.

Resistance formula

ρ = resistivity, l = length, A = cross-sectional area.

Membrane Resistance

Combined effect of R_lipid bilayer (high resistance) and R_channels (lower resistance).

Time Constant (τ)

Time required for voltage to reach 63% of its final value after a current is injected.

Voltage Change Over Time

Follows an exponential equation.

Time Constant Benchmarks

1τ = 63%, 2τ = 85%, 3τ = 95%, 4τ = 98%, 5τ = 99.3%, 6τ = 99.7%.

Smaller τ

Indicates faster response.

Larger τ

Indicates slower response.

Current Injection in Cells

Injecting current changes the voltage across the cell membrane.

Graph Shape

Starts at baseline (V₀), gradually rises to a new steady voltage (V_final).

Voltage Equivalence

V_inside - V_outside = voltage across membrane.

Key Terms to Know

Membrane potential, Capacitor, Resistor, Time constant (τ), Steady-state, RC circuit, Voltage response to current injection.