# Incandescent Lamp

Incandescent lamp with temperature dependent resistance

• Library:
• Simscape / Electrical / Passive

## Description

The Incandescent Lamp block models an incandescent lamp, the key characteristic of which is that the resistance increases as the filament warms up.

Under the simplifying assumption that the rate of heat loss from the filament is proportional to temperature difference to ambient, the temperature of the filament is governed by

`$k{t}_{c}\frac{dT}{dt}={i}^{2}R-kT$`

and the filament resistance is governed by the following equation

`$R={R}_{0}\left(1+\alpha T\right)$`

where:

• R0 is the initial resistance at turn-on (when filament is at ambient temperature).

• T is the filament temperature relative to ambient temperature.

• α is the resistance temperature coefficient.

• tc is the thermal time constant.

• k is the heat transfer coefficient.

• R is the filament resistance.

• i is the filament current.

There are two parameterization options:

• If you select `Specify resistance values directly`, the block uses values that you provide for filament resistance when on and at turn-on to determine the value for the heat transfer coefficient.

• If you select `Specify currents`, the block uses values that you provide for filament current when on and at turn-on to determine the value for the heat transfer coefficient.

Optionally you can specify a simulation time at which the lamp fails by providing a finite value for the Simulation time for open circuit fault event parameter on the Faults tab. When in the open-circuit state, the lamp resistance is set to be the value of the Open-circuit resistance parameter.

## Ports

### Conserving

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Electrical conserving port associated with the lamp positive voltage.

Electrical conserving port associated with the lamp negative voltage.

## Parameters

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### Resistance

Select one of the following methods for block parameterization:

• ```Specify resistance values directly``` — Provide the values for filament resistance at turn-on and when on in steady state. The block determines the value for the heat transfer coefficient based on these values. This is the default option.

• `Specify currents` — Provide the values for filament current at turn-on and when on in steady state. The block determines the value for the heat transfer coefficient based on these values.

The resistance seen by the external circuit when the lamp is initially turned on.

#### Dependencies

This parameter is visible only when you select `Specify resistance values directly` for the Parameterization parameter.

The resistance seen by the external circuit when the lamp is on and in steady state. This resistance should be greater than the Initial resistance at turn-on.

#### Dependencies

This parameter is visible only when you select `Specify resistance values directly` for the Parameterization parameter.

The current through the lamp when it is initially turned on.

#### Dependencies

This parameter is visible only when you select `Specify currents` for the Parameterization parameter.

The current through the lamp when it is on and in steady state. This current should be less than the Inrush current at turn-on.

#### Dependencies

This parameter is visible only when you select `Specify currents` for the Parameterization parameter.

The rated voltage for the lamp, and the voltage value for which the resistance or current values are provided in the on and turn-on states.

The fractional increase in resistance per unit increase in temperature.

### Dynamics

The first-order thermal time constant for filament temperature when the lamp is turned on or off.

Select between `On` and `Off`.

### Faults

Whether to enable open circuit fault.

For simulation times greater than this parameter value the filament resistance becomes equal to the Open-circuit resistance. Specifying a finite value for this parameter lets you simulate the fault dynamics when the bulb burns out.

#### Dependencies

To enable this parameter, set Enable open circuit fault to `On`.

The value of the filament resistance used when the lamp goes open-circuit.

#### Dependencies

To enable this parameter, set Enable open circuit fault to `On`.