Components in Series & Parallel Circuits

What an I-V graph shows

• An I-V graph plots the current through a component (y-axis) against the voltage across it (x-axis), with the voltage varied from negative through zero to positive
• The shape of the line tells you how the component's resistance changes with the voltage applied:
  • A straight line through the origin means the current is directly proportional to the voltage. The resistance is constant (this is ohmic behaviour)
  • A curved line through the origin means the current is not directly proportional to the voltage. The resistance is variable (this is non-ohmic behaviour)
• The resistance at any point on an I-V graph is given by R = V / I, not by the gradient. (For an ohmic conductor R = 1/gradient because the line is straight, but in general the V/I ratio at each point is what matters.)

I-V graph for a fixed resistor (or a metal wire at constant temperature)

• A straight line through the origin, because current and voltage are directly proportional, in both polarities
• The slope is the same everywhere, so the resistance is the same everywhere; fixed resistors and wires at a steady temperature are ohmic conductors

I-V graph for a filament lamp

• The curve passes through the origin, but it flattens off as the voltage and current grow; the same shape appears in reverse on the negative side
• A flatter slope corresponds to a higher resistance (because R = V / I and V grows faster than I)
• The physics: a larger current heats the filament; the metal ions then vibrate more vigorously, scattering the drifting electrons more often, so the resistance climbs
• A filament lamp is therefore a non-ohmic component, because its resistance is not constant across its working range

I-V graph for a semiconductor diode

• The diode is a one-way conductor: it lets current pass in the direction of its arrowhead symbol only, which is called forward bias
• In forward bias, almost no current flows until the voltage exceeds about 0.6–0.7 V; past that threshold, the current climbs very sharply with very little extra voltage. The resistance is effectively infinite below the threshold and very small above it
• In reverse bias, no current flows at all (over the normal operating range); the diode's resistance is enormous
• The I-V graph therefore sits flat on the V axis for negative V, hugs the V axis from 0 to about 0.6 V, then rises almost vertically

Investigating an I-V curve in the lab

• Apparatus:
  • the component under test (resistor, filament lamp or diode)
  • an ammeter wired in series with the component to read the current through it
  • a voltmeter wired in parallel across the component to read the voltage across it
  • a variable resistor in series with the component to vary the current
  • a cell or low-voltage supply
• Method:
  1. Build the circuit and set the variable resistor to its highest resistance (so the initial current is small)
  2. Record the voltmeter and ammeter readings
  3. Reduce the resistance of the variable resistor by a small step; record V and I again
  4. Repeat until a wide range of voltages has been swept (do not exceed the rated voltage of the component, or it may burn out)
  5. To capture the negative side of the curve, reverse the cell's connections and repeat
• Plot I against V with the recorded data points and join them with a smooth curve