# Series R-L Circuit - Charge/Discharge described properly?

Tags:
1. Nov 8, 2014

### James Craig

Hi

Rather than ask how it works iv'e studied this a bit (via conflicting sources) and hoping that another member could have a quick scan over and pick out any bits where ive got it wrong?

I know its a lot to read, but iv'e tried to keep it as short as possible, so if you could help i'd be very grateful !

SERIES R-L CIRCUIT

Discharged inductor with voltage applied:

‘Charging’ inductors store electrical energy, as potential energy, whilst creating a magnetic field, produced by a flow of current through the inductor.

Instantaneous:

Inductor characteristics

An inductor cannot build a magnetic field the instant voltage is applied, at this point it acts as an open circuit which means current cannot flow and maximum voltage is dropped across its terminals.

Resistors characteristics

As there is no current flow the potential difference across the resistor is zero.

The potential difference over the resistor is proportional to the current flowing through it.

The sum of the resistor and inductors voltage drops maintain equilibrium with source EMF.

Transient period:

Inductor characteristics

Current flow begins to increase and this changing current creates a changing magnetic field.

The changing magnetic field stores electrical energy as potential energy and induces a ‘back’ EMF which opposes the source EMF and the changing (increasing) flow of current.

The inductors magnetic field strength, its capacity to store energy and the induced EMF’s ability to oppose current flow are proportional to the rate at which the current is changing through the inductors coil.

This causes two outcomes:
Exponential decay of potential difference across the inductor.
Exponential growth of current through the inductor

Resistors characteristics

Current flowing through this series circuit is a constant, growing exponentially.

Potential difference over the resistor is proportional to the current flowing through it, growing exponentially.

The sum of the resistor and inductors voltage drops maintain equilibrium with source EMF.

Inductor characteristics

When steady state is reached, the inductor cannot store any more energy within its magnetic field and the potential difference across the inductor terminals is now zero.

The inductor is now acting like a short circuit with current flow through the circuit at its maximum.

Without a changing current there is no longer a changing magnetic field to induce an EMF, therefore there is no opposition to the current flow.

Resistors characteristics

Current flowing through a series circuit is constant, maintained at its maximum.

As potential difference over the resistor is proportional to the current flowing through it, maintained at its maximum.

The sum of the resistor and inductors voltage drops maintain equilibrium with source EMF.

‘Charged’ inductor with voltage removed:

‘Discharging’ inductors releases potential energy, as electrical energy, from its collapsing magnetic field, which induces an EMF within the inductor.

Instantaneous:

Inductor characteristics

The inductor cannot release all of its stored energy, from its magnetic field, in the instant voltage is removed.

As the source EMF is no longer acting on the inductor its polarity will reverse and, as the potential difference is still at its maximum, the magnitude of the voltage is maximum but now of negative value.

The energy stored within the magnetic field induces an EMF which opposes changing current, to maintain the current flow.

Resistors characteristics

The potential difference across the resistor is maintained in proportion with the current flow through the circuit.

Transient period:

Inductor characteristics

Current flow begins to decrease and the changing current creates a changing magnetic field.

The changing magnetic field releases potential energy as electrical energy ad induces an EMF, acting as source, which opposes the changing (decreasing) current.

The inductors magnetic field strength, its stored energy and the induced EMF ability to maintain the current are proportional to the rate at which the current is changing through the inductors coil.

This causes two outcomes:

Exponential decay of negative potential difference across the inductor.

Exponential decay of current through the inductor

Resistors characteristics

Current flowing through a series circuit is constant through all components, decaying exponentially in this case.

As potential difference over the resistor is proportional to the current flowing through it, decaying exponentially.

The sum of the resistor and inductors voltage drops maintain equilibrium at Zero volts.

Inductor characteristics

When steady state is reached, there is no longer a changing current to maintain the magnetic field, all previously stored energy within it has been released and an induced EMF will not exist.

As an EMF does not exist within the circuit the current flow and potential difference is Zero.

Resistors characteristics

As an EMF does not exist within the circuit the current flow and potential difference is Zero.

2. Nov 8, 2014

### sophiecentaur

The Energy stored in an Inductor is normally considered to be Kinetic in nature and not Potential. In the mechanical mass-on-spring analogue, the Capacitor is the equivalent to the Potential energy stored in a spring and the L is the equivalent to the Mass, with the KE being equivalent to the Field due to the Current in the Inductor.

Your post is way too long to be readable. What (I think) you are saying can be summed up in just a few lines of Maths and a simple differential equation, which describes the whole process as a function of time. You say you have kept it as short as possible and managed to prove that the verbal description is really not worth getting involved with. Just get into the Maths if you want to understand what's happening.