How do you solve cable equations?

How do you solve cable equations?

λ = r m r e + r i and τ = r m c m , where ri and re are the intracellular resistance (in Ω/cm) and extracellular resistance (in Ω/cm). The values rm and cm are the membrane resistance (in Ω/cm) and membrane capacitance (in F/cm), respectively.

What is the purpose of cable theory?

The main purpose of cable theory is to understand this process, i.e. how electrical signals from different synapses are combined in the system of branching tubes of different diameters and membrane properties that forms the dendritic tree of a cell.

What do you mean by cable model?

Classical cable theory uses mathematical models to calculate the electric current (and accompanying voltage) along passive neurites, particularly the dendrites that receive synaptic inputs at different sites and times.

Who discovered cable theory?

William Thompson (Lord Kelvin) developed cable theory in the 1850s as a way to model the decay of signals along underwater telegraph cables. Hodgkin and Rushton applied it to passive conduction along axons (Hodgkin and Rushton, 1946).

What are cable properties?

– properties of the nerve; axon, cell body and dendrite that affect distance and speed of a membrane potential. – passive conduction properties are called cable because they are analogous to properties of long copper telecommunication cables (before satellites)

What is cable theory of nerve conduction?

On the basis of this equivalent circuit model, the conduction of the nerve is often described by using a theory in which the conduction is regarded as an electric current on imaginary electric longitudinal leads running inside and outside the axon membrane, known as a cable theory (Koch, 1984).

What are the cable properties?

The electrotonic properties of neurons that underlie the spread of electrical current are often referred to as cable properties. Electrotonic theory was first applied mathematically to the nervous system in the late 19th century for spread of electric current through nerve fibers.

What is axial resistance?

axial resistance is the internal resistance to flow: the larger the diameter of the structure, the more opportunity there is for the ions to flow. therefore, neurons with lower axial resistance (larger diameter) will have longer length constants.

What are Ranvier’s nodes?

Node of Ranvier, periodic gap in the insulating sheath (myelin) on the axon of certain neurons that serves to facilitate the rapid conduction of nerve impulses. Nodes of Ranvier are approximately 1 μm wide and expose the neuron membrane to the external environment.

How to calculate the sizing of a cable?

Formula is: I=Load (in kW)/ (sqrt (3) V (in kV) p.f) (A) The current obtained has to derated since the cable is designed to operate at a defined temperature. Derating factors will be available in cable catalog. Get the cable size corresponding to this derated current from the catalog.

How to calculate the power loss of a cable?

Calculation of the power loss within the cable is given by: P = Ib^2 * R * n (i.e. the current squared, times the resistance) Again with our resistance and reactance being per unit length, we need to multiple by the cable length to get the final power loss.

How to calculate voltage drop and size of electrical cable?

Full Load Current = (100 · 1000) / (1.732 · 415) = 139 Amp. For selection of proper cable following conditions should be satisfied: Cable derating amp should be higher than full load current of load.

How to calculate the speed of a coaxial cable?

I leave it to other sources to provide the complex equations needed to precisely model coaxial cables. a = outside radius of inner conductor (inches) c = speed of light in a vacuum = 299,792 km/s = 186,282 mi/s ε0 = permittivity of free space = 8.85419×10 -12 F/m