Practical: Investigating I-V Characteristics

The Resistance Equation

The resistance of a component can be calculated using the formula:

$$V = I \times R$$

Where:

• $V$ = potential difference in Volts (V)
• $I$ = current in Amperes (A)
• $R$ = resistance in Ohms ($\Omega$)

Worked Example: Calculate the resistance of a component.

Step 1: Record $V$ from the voltmeter and $I$ from the ammeter.

• $V = 6.0\text{ V}$
• $I = 0.5\text{ A}$

Step 2: Rearrange the formula and substitute the values.

• $R = \frac{V}{I}$
• $R = \frac{6.0}{0.5}$

Step 3: Calculate the final answer with units.

• $R = 12.0\text{ }\Omega$

The Potential Divider Advantage

• Why might a standard series circuit fail to give you a complete set of data?
• A simple variable resistor in series cannot achieve a potential difference of exactly $0.0\text{ V}$ across the test component, as this would require the variable resistor to have infinite resistance.
• A potential divider (also called a potentiometer circuit) is a superior alternative for investigating I-V characteristics because it allows the potential difference to be smoothly varied from $0\text{ V}$ up to the full supply voltage.
• It uses all three terminals of a variable resistor. The power supply is connected across the two fixed ends, and the test component is connected in a parallel branch using the sliding contact (wiper).

Investigating I-V Characteristics (Required Practical 4)

• How do we prove exactly how a component responds to changes in voltage?

• To investigate a component's characteristics, you must collect at least 6 to 10 pairs of readings in the positive direction and a similar set in the negative direction.

• Step 1: Set up the standard test circuit and check that the meters read zero before closing the switch to avoid a zero error.

• Step 2: Record the starting potential difference and current.

• Step 3: Adjust the variable resistor to change the potential difference and record the new readings, repeating this for 6–10 positive data points.

• Step 4: Switch the circuit off between readings. This controls the temperature, preventing the component from heating up (which would change its resistance).

• Step 5: To obtain negative values, reverse the connections at the battery or power pack terminals. Both meters will now display negative values, allowing you to plot the 3rd quadrant of the graph.

I-V Graphs: Fixed Resistors

• Not all electrical components behave the same way when you push a current through them.
• A fixed resistor is an Ohmic conductor (a linear component).
• Its I-V graph is a straight line that passes directly through the origin $(0,0)$, showing that current is directly proportional to the potential difference.
• This direct proportionality only holds true if the temperature is kept perfectly constant.
• On an I-V graph with $I$ on the y-axis and $V$ on the x-axis, the gradient is equal to $1/R$. A steeper line indicates a lower resistance, while a shallower line indicates a higher resistance.

I-V Graphs: Filament Lamps

• A filament lamp is a non-Ohmic conductor.
• Its I-V graph is an S-shaped curve that passes through the origin. It mirrors itself symmetrically in the negative quadrant because resistance depends on the magnitude of the current, not its direction.
• As the potential difference increases, the current increases, which causes the temperature of the filament to increase.
• Higher temperatures cause the positively charged lattice ions in the metal to vibrate more vigorously.
• This increases the frequency of collisions between free electrons and the lattice ions, which increases the resistance. As a result, the current increases at a slower rate than the potential difference.

I-V Graphs: Diodes and LEDs

• A diode is a non-Ohmic conductor that only allows current to flow in one direction, known as the forward bias.
• In the reverse bias (connected in the wrong direction), the resistance is extremely high and the current is strictly zero.
• Current only begins to flow in the forward direction once a threshold voltage is reached (typically $0.6\text{ V}$ to $0.7\text{ V}$ for silicon diodes).
• The I-V graph is perfectly horizontal along the x-axis for all negative voltages and positive voltages below the threshold, before rising very steeply once the threshold is crossed.
• When testing a diode, a milliammeter must be used because the initial currents are very small. A protective fixed resistor (e.g., $100\text{ }\Omega$) must also be added in series to prevent the diode from burning out, though the voltmeter must be placed in parallel across only the diode.