Question

Can someone pls show me the VR (Voltage-Resistance) Graphs for an NTC thermistor, filament lamp and conductors?

How do these components' resistances vary with voltage?

Answer 1

Please see below.

Explanation:

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Let's take a look at an NTC thermistor circuit:

The input of `12` volts goes through a voltage regulator that regulates and supplies `V_s=5` volts as supply voltage to the circuit. The temperature sensor measures the change in the output voltage as a result of the change in the resistance of the element in the sensor and converts it into the desired unit .

We know that the circuit has a fixed resistor `(R)` of `10kOmega` and the resistor in the thermistor element `(R_t)` also has a value of `10kOmega` at the nominal ambient temperature of `21^@ C`.which varies with temperature.

The output voltage `V_o` varies as `R_t` varies. The relationship between them is:

`R_t=R(V_s/V_o-1)`

It is difficult to find the Voltage-Resistance graph of an NTC thermistor in books but we can develop it here. We will designate the horizontal axis as the `V_o`-axis and the vertical one as the `R_t`-axis.

Furthermore, in order to obtain a reasonably clear scale, we will consider the two resistances in the equation in units of `10KOmega` instead of `Omega`. This is like dividing both sides of the equation by `10000`. As such, our equation becomes::

`R_t=R(5/V_o-1)` or

`R_t/R=5/V_o-1` which we will graph.

The graph will be:

But since we are dealing with positive voltages only, we will concern ourselves with the right hand side of the graph where both `V_o` and `R_t` are positive. We will also limit the domain to `0 <= V_o <= 5`. Therefore, we will have:

As the graph shows, when `V_o=0`, `R_t=oo` and when `V_o=5`, `R_t=0`. In between these values, the graph shows how the output voltage varies as the resistance of the thermistor element changes.

As far as filament lamps go, here are some graphs:

As far as metallic conductors go, their voltage-current, current-resistance and voltage-resistance relationships are linear and their graphs are straight lines that go through the origin. They are called Ohmic conductors:

Hope this helps.