Physics (9630) | Current–voltage characteristics

⚡ Current-Voltage Characteristics: How Components Behave ⚡

Welcome to the chapter on Current–voltage characteristics! Don't worry if this sounds complex—it’s simply how we graphically represent the relationship between the voltage across a component (like a bulb or resistor) and the current flowing through it.

Understanding these graphs, often called I–V curves, is crucial because they tell us immediately whether a component's resistance is fixed or whether it changes depending on how much power it uses. This forms the backbone of circuit analysis!

Review: The Essential Triangle (V, I, R)

Before diving into the graphs, let's quickly remember the foundation concepts from the previous section (3.4.1):

• Voltage (V): Potential difference (pd). Energy transferred per unit charge (work done per unit charge). Measured in Volts (V).
• Current (I): Rate of flow of charge. Measured in Amperes (A).
• Resistance (R): Opposition to current flow. Defined by \(R = V / I\). Measured in Ohms (\(\Omega\)).

3.4.2 Ohmic Conductors and Ohm’s Law

What is Ohm’s Law?

Ohm’s Law is often mistakenly stated as \(V=IR\). While this equation defines resistance, Ohm's Law itself is a statement about proportionality.

Ohm’s Law states that the current (I) through a conductor is directly proportional to the potential difference (V) across it, provided that physical conditions, such as temperature, remain constant.

Mathematically: $$ I \propto V \quad \text{ (under constant physical conditions)} $$

The I–V Characteristic of an Ohmic Conductor

A component that obeys Ohm's Law is called an ohmic conductor (e.g., a standard resistor at a constant temperature).

Graph Shape:

The I–V characteristic for an ohmic conductor is a straight line passing through the origin.

• Why a straight line? Because \(R = V/I\) is constant. If you double V, you double I.
• Why through the origin? If there is no voltage (V=0), there is no current (I=0).

Analogy: Imagine a perfectly smooth, straight road. The faster you push your car (V), the faster it goes (I). The friction (R) never changes.

3.4.2 Non-Ohmic Conductors

Many common electrical components do not have constant resistance. Their I–V characteristics are curves, meaning they are non-ohmic.

1. The Filament Lamp (Light Bulb)

A filament lamp contains a thin wire (often tungsten). As the current increases, the wire heats up dramatically (it glows white hot!).

Graph Shape and Explanation:

The I–V graph for a filament lamp is a curve that bends towards the V-axis (or flattens if I is on the Y-axis).

• Observation: As V and I increase, the gradient of the graph decreases (if V is on Y and I is on X).
• Physics: Increased current leads to increased heating (due to energy dissipation, \(P=I^2R\)).
• Effect: For metals, resistance increases with temperature. The higher temperature means the positive metal ions vibrate with greater amplitude, increasing the frequency of collisions with the flow of charge carriers (electrons).
• Result: A larger voltage increase is required to produce the same increase in current. The resistance of the bulb increases as it gets hotter.

Did you know? The operating temperature of a typical tungsten filament is over 2500 °C! This change in physical condition (temperature) is why Ohm's Law does not apply here.

2. The Semiconductor Diode

A diode is a component designed to control the direction of current flow. It is the perfect example of a non-ohmic device whose resistance depends heavily on the polarity of the applied voltage.

Graph Shape and Explanation:

The diode characteristic has three distinct regions:

1. Forward Bias (Positive Voltage):
   • For low positive voltages (V), almost no current flows.
   • Once the voltage reaches the threshold voltage (or 'turn-on' voltage, typically about 0.6 V for silicon), the resistance drops rapidly, and current increases exponentially.
2. Reverse Bias (Negative Voltage):
   • The resistance is extremely high (ideally infinite).
   • Almost zero current flows, regardless of how large the negative voltage becomes (until a very high breakdown voltage, which is usually ignored at this level).

Analogy: A diode is like a one-way gate. It stays firmly shut until you push hard enough (threshold voltage), then it swings wide open. If you push from the wrong side (reverse bias), it stays locked tight.

Interpreting I–V Graphs: The Resistance Challenge

When analyzing an I–V graph, remember that Resistance \(R\) is defined by \(V/I\). However, the way you calculate R from the gradient depends entirely on which variable is plotted on which axis.

A Note on Ideal Meters (Syllabus Requirement)

Unless a question specifically tells you otherwise:

• An Ammeter should be treated as ideal (having zero resistance).
• A Voltmeter should be treated as ideal (having infinite resistance).

Case A: V on the Y-axis, I on the X-axis

This layout is mathematically standard (Y vs X).

Gradient \(m = \Delta V / \Delta I\)

Therefore, the gradient equals the resistance (R).

$$ m = R $$

Case B: I on the Y-axis, V on the X-axis

This layout is common in physics when discussing non-ohmic devices.

Gradient \(m = \Delta I / \Delta V\)

This value (\(I/V\)) is the reciprocal of resistance, known as conductance (\(G\)).

Therefore, the gradient equals \(1/R\).

$$ m = \frac{1}{R} $$

Memory Aid: Always check the axes first! If the graph is steep, is resistance high or low? If the slope is large (Case B: I vs V), \(1/R\) is large, so \(R\) is small. If the slope is large (Case A: V vs I), \(R\) is large.

Calculating Resistance from a Non-Ohmic Curve

For a non-ohmic component (like a lamp or diode), resistance is not constant. You must calculate the resistance at a specific operating point \((V_1, I_1)\).

At any point on the curve: $$ R = \frac{V_1}{I_1} $$

Example: If a filament lamp has 2 V across it when 0.5 A flows, the resistance at that point is \(R = 2 \text{ V} / 0.5 \text{ A} = 4 \ \Omega\). If the voltage is increased to 10 V and the current only reaches 1.0 A, the resistance is now \(R = 10 \text{ V} / 1.0 \text{ A} = 10 \ \Omega\). This confirms the resistance increases.