# Current-voltage Characteristics

## Current-voltage Characteristics Revision

**Current-voltage Characteristics**

For the AQA course you are expected to describe **Ohm’s Law** and identify how it can be investigated. You are also expected to recognise and explain in detail the V-I graphs for **ohmic conductors**, **filament bulbs** and **semiconductor diodes**.

**Ohm’s Law**

**Ohm’s law** states “the **current** through a **conductor** is proportional to the **potential difference** across it”. This law only applies if the conductor is kept at a constant **temperature** as changes in temperature affects **resistance**. This law can be represented in the equation:

V=IR

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

As a results, V \propto I when R is kept constant by maintaining a constant temperature.

A circuit just like the one below can be used to investigate **Ohm’s law**:

It is important to note that for a **constant temperature** to be maintained, the switch should only be closed for a very short period of time whilst measurements are being taken and then switched off. This is because the components of the circuit heat up while a **current** flows through them.

Using the circuit above, the **variable resistor** can be used to vary the **current** and **potential difference**. Pairs of readings for **current** and **potential difference** can be taken then **resistance** calculated using R=\dfrac{V}{I}.

For a component to obey **Ohm’s law**, when current is plotted against voltage, it should produce a linear graph through the origin similar to the one shown:

The **resistance** of the graph can be calculated by finding the inverse of the gradient.

**I-V Graph for an Ohmic Conductor**

We have already seen the I-V graph for an **Ohmic conductor **such as a **resistor** at fixed **temperature**. The graph should look like the one below for an **Ohmic conductor**:

The graph shows the **Ohmic conductor** has a directly proportional relationship between **current** and **potential difference**. The resistance of the graph is given by \dfrac{1}{gradient}.

**I-V Graph for a Filament Lamp (Non-ohmic)**

A filament lamp requires high temperatures to cause the filament inside the lamp to glow, producing light. The I-V graph is shown below:

The central part of the I-V graph for a **filament lamp** is linear, this only applies at very low **potential difference**. However, the graph then curves towards the axis for pd, indicating an increase in **resistance** (as a high increase in pd does not change current).

The change in resistance is caused by an increase in **temperature**. As the temperature of the filament lamp increases, its **resistance** also increases. As temperature increases, the particles in the filament vibrate more, increasing the resistance as the free electrons are more likely to collide with the atoms.

**I-V Graph for a Semiconductor Diode**

The I-V graph for a **semiconductor** diode is distinctive and looks very different from the previous two graphs. The shape of the graph is linked to the function of the **diode**. A **diode** is used in a circuit to prevent **current** flowing in the wrong direction around a circuit. The graph can be seen below:

For negative **potential differences,** zero **current** is able to flow. This is because a **forward bias **only allows current to pass through in the forwards direction.

At low positive **potential differences**, the **semiconductor diode** will not allow any current to pass through and therefore, the **current** remains zero.

At a specific **potential difference**, known as the **threshold voltage**, the **diode** rapidly allows large **currents to pass** through for small increases in **potential difference**. Most Silicon semiconductors have a **threshold voltage **of 0.7 \text{ V}.

## Current-voltage Characteristics Example Questions

**Question 1:** Describe a method you could use to demonstrate that a fixed resistor obeys Ohm’s law.

**[6 marks]**

To demonstrate that a fixed resistor obeys ohm’s law, **pairs of readings for current and voltage** need to be taken. A series circuit containing a power source, variable resistor, fixed resistor, an **ammeter in series** **and a voltmeter in parallel **can be used. A pair of readings should be taken when the **variable resistor is set to its minimum resistance**. Then the variable resistor should be changed slightly and a new pair of readings taken. This should be repeated for at **least 5 pairs of readings of V and I**. Resistance can be calculated using \bold{V=IR}.

It is important to keep the temperature constant so the circuit needs to be **switched on for as short a period of time as possible to prevent heating. **A graph of V against I could be plotted. It should show a straight line through the origin as it obeys Ohms law.

**Question 2:** Describe and explain the I-V graph for a semiconductor diode.

**[3 marks]**

For negative potential differences, the **current is zero as a diode only allows current to flow in the forward direction**. At low positive potential differences, the current remains zero as it has not met the **threshold voltage** which is a certain minimum voltage needed for current to pass through a diode. Once the threshold voltage has been met, the **current rapidly increases **as resistance decreases.

**Question 3:** Describe why the shape for a filament bulb I-V graph is seen.

**[2 marks]**

At low potential differences in both directions, the filament bulb acts as an **Ohmic conductor**, hence the straight line through the origin. At higher potential differences, the graph curves as **temperature and resistance increases**.