Worksheet 5: Ohm’s Law and DC Circuits¶

Understanding the fundamental principles of electrical circuits is crucial in physics and engineering. This lab focuses on Ohm’s Law, the behavior of resistors and Light Emitting Diodes (LEDs) in circuits, and the measurement of resistivity in conductive materials. These principles help us analyze voltage, current, and resistance in different electrical components and configurations.

Ohm’s Law¶

Ohm’s Law describes the relationship between voltage $V$ , current $I$ , and resistance $R$ :

$V = IR$

This equation shows that the current flowing through a resistor is directly proportional to the applied voltage and inversely proportional to its resistance. In this lab, we will verify Ohm’s Law experimentally using different resistors.

Resistors and Their Properties¶

Resistors obey Ohm’s Law and can be characterized by their resistance value (measured in Ohms, $\Omega$ ). Resistance depends on the material’s resistivity ( $\rho$ ), the resistor’s length ( $L$ ), and its cross-sectional area ( $A$ ):

$R = \rho \frac{L}{A}$

This relationship is crucial for measuring resistivity, as explored in Measurement 3 of this lab.

Light Emitting Diodes (LEDs)¶

Unlike resistors, LEDs are non-Ohmic components, meaning their current-voltage ( $I$ - $V$ ) relationship is nonlinear. LEDs have a turn-on voltage, below which they do not conduct. The I-V characteristic curve of an LED differs from that of an Ohmic resistor, and we will analyze these differences experimentally.

Measurement Instruments¶

To accurately measure voltage, current, and resistance, we will use Digital Multimeters (DMMs): - Ammeter (DMM in current mode): Measures current; must be connected in series with the circuit. - Voltmeter (DMM in voltage mode): Measures voltage; must be connected in parallel across a circuit element.

Additionally, we will use a DC power supply to control the voltage applied to the circuits and set current limits to protect sensitive components like LEDs.

Objectives¶

By the end of this lab, you will be able to:
- Experimentally verify Ohm’s Law using resistors.
- Investigate the I-V characteristics of LEDs, identifying their turn-on voltage and non-Ohmic behavior.
- Measure the resistivity of conductive wires and analyze its dependence on length and cross-sectional area.
- Develop proficiency in using Digital Multimeters (DMMs) for voltage, current, and resistance measurements.

Materials List¶

DC Power Supply (variable voltage, current-limited)
Digital Multimeters (DMMs) (used as ammeter and voltmeter)
Resistors: 220 Ω, 1 kΩ
Light Emitting Diodes (LEDs): Green LED, Yellow LED
Breadboard
Connecting Wires/Cables
Resistance Wire Board

Measurement 1: Verification of Ohm’s Law for Ohmic Resistors¶

You will set up simple circuits containing 220 Ω and 1 kΩ resistors and measure the voltage across and current through these resistors.
By varying the voltage in small steps and recording current values, you will plot I-V curves to determine whether the resistors obey Ohm’s Law.
Resistance will be calculated from the slope of the I-V graph and compared to direct resistance measurements taken using a DMM in resistance mode.

Measurement 2: I-V Characteristics of LEDs¶

The electrical behavior of Light Emitting Diodes (LEDs) will be examined by measuring their current-voltage (I-V) characteristics.
You will construct a circuit with an LED in series with a current-limiting resistor and record voltage and current values as the voltage is increased.
The turn-on voltage (the voltage at which the LED starts conducting) will be identified.
The non-Ohmic behavior of LEDs will be analyzed by comparing their I-V curve to that of resistors.

Measurement 3: Resistivity Measurement Using Resistance Wires¶

You will determine the resistivity ( $\rho$ ) of different wire gauges using a Resistance Wire Board.
Resistance values will be measured for different wire lengths, and a resistance vs. length graph will be created.
The slope of this graph, combined with known wire dimensions, will be used to calculate the material’s resistivity and compare it to expected theoretical values.

Resistivity of Kanthal A-1¶

The wire material we use on the wire resistivity board is Kanthal A-1, and according to the manufacturer the electrical resistivity at 20°C is $1.45\, \Omega \, \text{mm}^2/m$ .