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Circuits overview

Topic 3 of 9

I-V curves and temperature

A component characteristic connects its current and p.d. under specified conditions. Temperature, settling and polarity can change the relationship, so a graph needs more than the component's name.

Here current is vertical and p.d. horizontal. On a straight line through the origin, gradient I/V is 1/R. On a curved graph, calculate the operating resistance as V/I at that point. A local tangent describes a small change in current per change in voltage, which is a different ratio. If the axes are reversed, reconsider the gradient interpretation.

Ohmic conductor at fixed temperature

Ohmic conductor at fixed temperatureOhmic conductor at fixed temperature. Current in A is vertical and voltage in volts is horizontal. The model has the stated odd reverse branch and is restricted to minus three to plus three volts. Dots identify the supplied nonnegative readings; the smooth line is a teaching model, not an experimental fit.-3-2-10123-0.15-0.1-0.0500.050.10.15Current I / AP.d. V / V

A constant gradient here means constant resistance: 20 ohm. Temperature and the other physical conditions are fixed.

A settled filament lamp

A settled filament lampA settled filament lamp. Current in A is vertical and voltage in volts is horizontal. The model has the stated odd reverse branch and is restricted to minus three to plus three volts. Dots identify the supplied nonnegative readings; the smooth line is a teaching model, not an experimental fit.-3-2-10123-0.2-0.100.10.2Current I / AP.d. V / V

The filament warms as current increases. Read V/I at a point for its resistance; this curved graph has no single constant resistance.

A self-heating NTC thermistor model

A self-heating NTC thermistor modelA self-heating NTC thermistor model. Current in mA is vertical and voltage in volts is horizontal. The model has the stated odd reverse branch and is restricted to minus three to plus three volts. Dots identify the supplied nonnegative readings; the smooth line is a teaching model, not an experimental fit.-3-2-10123-30-20-100102030Current I / mAP.d. V / V

These readings include self-heating. A low-current test that holds its temperature fixed is a different comparison. Notice the milliampere axis.

Diode: a qualitative characteristic

Diode: a qualitative characteristicCurrent is vertical and anode-minus-cathode p.d. horizontal. Reverse current is small and negative before breakdown. Forward current rises steeply at positive p.d. No numerical threshold or reverse breakdown region is specified, and the reverse curve is not a mirror of the forward curve.Current IAnode-to-cathode p.d.0ReverseForwardSmall current

The axes have no numerical scale. The forward behaviour depends on the diode and its conditions; do not infer a universal turn-on voltage.

These are supplied teaching models with named conditions and separate current scales. The ohmic, lamp and self-heated NTC examples use symmetric reversal; the diode does not. Smooth interpolation illustrates shape, not additional measured points or a universal component calibration.

Ohmic resistor: fixed physical conditions

A straight line through the origin represents proportional I and V. A 20.0 Ω model gives 0.050, 0.100 and 0.150 A at 1.00, 2.00 and 3.00 V. Each V/I is 20.0 Ω. Significant heating would violate the fixed-temperature comparison.

Filament lamp: settled heating changes resistance

As voltage magnitude increases, current heats the metal filament. Its resistivity rises, so current increases less rapidly and the I-V curve becomes less steep. The supplied settled model gives:

At 1.00 V, I = 0.100 A: R = 10.0 Ω
At 2.00 V, I = 0.160 A: R = 12.5 Ω
At 3.00 V, I = 0.200 A: R = 15.0 Ω

A cold filament's initial response is not the same as its settled operating characteristic. Do not predict an exact lamp current by assuming it keeps one fixed resistance while heating.

Semiconductor diode: polarity matters

The diode conducts strongly in its forward direction once the applied voltage produces appreciable current. Reverse current is small over the shown range before breakdown. Do not mirror its forward branch to obtain the reverse branch or assign every diode one universal forward threshold.

The real characteristic is different from an ideal zero-drop conducting state and perfectly blocked reverse state. An ideal model is useful only when that approximation is stated.

NTC thermistor: identify the experiment

For a negative temperature coefficient thermistor, increasing temperature reduces resistance. In the supplied settled voltage sweep, self-heating increases as voltage magnitude rises, so current can rise progressively more steeply. At 1.00, 2.00 and 3.00 V, the model currents are 5.0, 14.0 and 30.0 mA, where 1 mA = 10-3 A:

R = 1.00/0.0050 = 200 Ω
R = 2.00/0.0140 ≈ 143 Ω
R = 3.00/0.0300 = 100 Ω

If temperature is instead externally controlled and self-heating is kept small, an approximately linear low-field I-V characteristic can be observed at that fixed temperature. These are different measurement conditions, not contradictory properties.

Why typical metals and NTC semiconductors differ

The carrier model I = nAvq separates carrier number density from mean drift speed. Compare the same geometry and applied electric field when discussing temperature:

  • Typical metal: greater lattice vibration increases carrier scattering. Carrier number density stays roughly unchanged, but mean drift speed decreases at the same field. Current decreases at the same p.d., so resistance and resistivity increase. Faster random thermal motion does not imply faster directed drift.
  • NTC semiconductor: warming makes more charge carriers available. Increased number density is the main explanation for its falling resistivity in this regime; it is not simply that the same carriers move faster. This is not a claim that every semiconductor resistance decreases under every condition.

If current is fixed instead of field, warming a typical metal requires a larger field and p.d. to maintain that current. State the controlled quantity before comparing the microscopic explanation with a circuit reading.

Obtain and interpret a characteristic

Use an adjustable low-voltage source or a suitable series control, an ammeter in the component path and a voltmeter across its terminals. Record actual I/V pairs with ranges, resolution and polarity. Choose suitable ratings and a limiting resistance for a diode. Reverse polarity deliberately for the reverse branch rather than changing graph signs without changing the circuit.

For a lamp characteristic, allow its thermal state to settle at each point. For a separate resistance-versus-temperature study, measure temperature, allow the sensor response to settle and keep unwanted electrical self-heating small. Record which condition was controlled; otherwise a temperature effect can be confused with a different voltage sweep.

Optional check Compare higher temperatures at the same applied electric field in a typical metal and in the stated NTC semiconductor. Which explanation is appropriate?
Compare higher temperatures at the same applied electric field in a typical metal and in the stated NTC semiconductor. Which explanation is appropriate?