Sketch and explain the current‑voltage (I‑V) graphs for:
a resistor of constant resistance,
a filament lamp,
a diode.
Key Concepts
Resistance \$R\$ is defined by Ohm’s law:
\$\$
V = IR
\$\$
For a material with constant \$R\$, the I‑V relationship is linear. If \$R\$ changes with temperature, the graph deviates from a straight line.
1. Resistor of Constant Resistance
Ideal metallic resistor: \$R\$ does not change appreciably over the range of applied voltage.
Quantity
Symbol
Relationship
Resistance
\$R\$
Constant
Current
\$I\$
\$I = \dfrac{V}{R}\$
The I‑V graph is a straight line passing through the origin with slope \$1/R\$.
Suggested diagram: Straight‑line I‑V graph for a constant‑resistance resistor (origin to top‑right).
2. Filament Lamp
A filament lamp is made of a metal (usually tungsten) whose resistance increases with temperature.
When current flows, the filament heats up, \$R\$ rises, and the I‑V curve bends.
Region
Behaviour
Low voltage
Filament cool → low \$R\$ → nearly linear.
Higher voltage
Filament hot → \$R\$ increases → curve flattens.
The graph starts from the origin, rises steeply, then becomes progressively less steep.
Suggested diagram: I‑V curve for a filament lamp – convex upward, starting at the origin and curving toward a horizontal asymptote.
3. Diode
A semiconductor diode allows current to flow readily in one direction (forward bias) and blocks it in the opposite direction (reverse bias).
Key points of the I‑V characteristic:
Forward bias: negligible current until the “turn‑on” (or “knee”) voltage \$Vk\$ is reached (≈ 0.6 V for silicon). Beyond \$Vk\$, current increases rapidly.
Reverse bias: only a very small leakage current flows (practically zero) until breakdown voltage is reached (normally not shown in IGCSE).
The idealised I‑V graph consists of three distinct sections:
Region A: Reverse bias – flat line near \$I=0\$.
Region B: Forward bias below \$V_k\$ – almost horizontal.
Region C: Forward bias above \$V_k\$ – steep rise.
Suggested diagram: Diode I‑V graph showing a near‑horizontal line in reverse bias, a “knee” at about \$0.6\,\$V, then a steep upward curve in forward bias.
Comparative Summary
Component
Resistance Behaviour
Shape of I‑V Graph
Constant‑R resistor
R constant
Straight line through origin (linear)
Filament lamp
R increases with temperature
Convex upward, slope decreasing as \cdot increases
Diode
Non‑ohmic; very high R in reverse, low R after turn‑on
Two‑piece graph: flat reverse, knee, then steep forward
Practical Tips for Sketching
Always start the graph at the origin for devices that have zero current at zero voltage (resistor, filament lamp). The diode does not conduct in reverse, so the reverse‑bias line is drawn at \$I\approx0\$.
Identify the region where the device obeys Ohm’s law – draw a straight‑line segment with slope \$1/R\$.
For devices whose resistance changes, indicate the curvature qualitatively rather than trying to plot exact values.
Label the “knee” voltage on the diode graph and note the approximate value for silicon (\$\approx0.6\,\$V) or germanium (\$\approx0.3\,\$V).
Common Misconceptions
Assuming a filament lamp has a constant resistance – it actually varies strongly with temperature.
Thinking a diode’s I‑V curve is a perfect straight line after the knee – the increase is exponential, but at IGCSE level a steep line is acceptable.
Confusing the direction of current flow in a diode – current flows from anode to cathode in forward bias only.
Exam Checklist
Can you draw a straight‑line I‑V graph for a constant resistor and label the slope as \$1/R\$?
Can you sketch the curved I‑V graph for a filament lamp and explain why it bends?
Can you produce the three‑region I‑V graph for a diode, indicating reverse bias, knee voltage, and forward‑bias region?
Can you state the physical reason for each graph’s shape?