V-I Characteristics

Where:

• $V$ = potential difference in volts ($\text{V}$)
• $I$ = current in amperes ($\text{A}$)
• $R$ = resistance in ohms ($\Omega$)

Worked Example

What is the resistance of a fixed resistor if a potential difference of $9.0\text{ V}$ produces a current of $0.03\text{ A}$?

Step 1: Identify the values.

• $V = 9.0\text{ V}$, $I = 0.03\text{ A}$

Step 2: Substitute into the rearranged equation ($R = \frac{V}{I}$).

• $R = \frac{9.0}{0.03}$

Step 3: Calculate.

• $R = 300\text{ }\Omega$

Filament Lamps and Lattice Vibrations

Every time you turn on a traditional light bulb, the metal wire inside heats up so intensely that it begins to glow.

As current flows through the filament, free conduction electrons collide with the positive metal ions in the solid lattice. These collisions transfer kinetic energy, causing the metal to heat up significantly.

As the temperature rises, the metal ions experience greater lattice vibrations, vibrating with higher frequency and amplitude. This makes it much harder for electrons to pass through, resulting in more frequent ion-electron collisions and a sharp increase in resistance.

Because its resistance changes, a filament lamp is a non-Ohmic conductor. Its $I$-$V$ graph forms an "S-shape" curve that passes through the origin; it is initially linear but flattens out at higher voltages as the resistance increases.

Diodes and Threshold Voltage

Imagine a turnstile at a football stadium that only allows people to walk through in one direction.

A diode is an electrical component that strictly enforces a one-way flow of current. It allows current to flow easily in forward bias, but has an extremely high resistance in reverse bias, meaning it does not allow current to flow backwards.

The $I$-$V$ graph for a diode is flat along the x-axis for negative voltages. Even in the forward direction, the current remains at exactly zero until a specific threshold voltage is reached.

For a standard silicon diode, this threshold is typically around $0.6\text{ V}$ to $0.7\text{ V}$. Once the potential difference pushes past this value, the resistance drops sharply and the graph curves steeply upwards. An LED (Light Emitting Diode) behaves identically but emits light, usually requiring a slightly higher threshold voltage of $1.5\text{ V}$ to $2.0\text{ V}$.

Investigating V-I Characteristics (Core Practical)

How do physicists actually prove these electrical rules in a school laboratory?

To test any component, you must build a circuit with an ammeter connected in series to measure the current, and a voltmeter connected in parallel across the component to measure the potential difference.

You can change the potential difference by adjusting a variable resistor or a variable power pack, and you can obtain negative readings by reversing the connections on the battery.

A crucial precaution during this experiment is to switch the circuit off between readings. This prevents the component from heating up, ensuring that a fixed resistor does not accidentally increase in resistance due to thermal effects.