Experiment #2 Ohm’s Law and Conservation of Energy

Objectives

To verify Ohm’s Law experimentally.
To understand the concept of power absorption and delivery associated with electrical elements.
To observe conservation of energy in a circuit.
To understand the power rating of a resistor.
To understand the Constant Voltage and Constant Current modes in DC Power Supply.
To familiarize with taking voltage and current measurements using a DMM.

Equipment

Breadboard
DC Power Supply
Digital Multimeter (DMM)

Background

I. Ohm’s Law

Under constant temperature condition, the voltage $\color{black}V$ between two points in a circuit is linearly proportional to the current $\color{black}I$ that flows from one point to the other, $\color{black}V \propto I$ . The proportionality constant, denoted by $\color{black}R$ , is the resistance between the two points considered. When Ohm’s Law is applied, passive sign convention must be taken into account, as shown in Figure 2 – 1.

Figure 2 – 1 Ohm’s Law with Passive Sign Convention

II. Conservation of Energy

The power absorbed or delivered by an electrical element is associated with the flow of charge and follows directly the definitions of voltage and current. The power $\color{black}P$ associated with an element is simply the product of the voltage $\color{black}V$ across the element and the current $\color{black}i$ that flows through the element, $\color{black}P = Vi$ . Similar to the application of Ohm’s Law, passive sign convention must be considered when power calculation is performed, as shown in Figure 2 – 2.

Figure 2 – 2 Power Calculation with Passive Sign Convention

To determine if a circuit element absorbs or delivers power, the sign of the calculated power $\color{black}P$ will be examined. If the calculated power is positive, $\color{black}P > 0$ , it can be concluded that power is absorbed by the element. On the other hand, if $\color{black}P \lt 0$ , the conclusion is the element delivers power.

The total power absorbed in a circuit should balance the total power delivered in the same circuit. Therefore, the aggregate power in a circuit should be zero. This means that the law of conservation of power is obeyed in a circuit.

III. Constant Voltage and Constant Current Modes in DC Power Supply

Figure 2 – 3 Channels 1 and 2 in constant voltage mode (green display); channel 3 in constant current mode (red display).

In most cases, the power supply unit operates in the constant voltage mode. In this mode, the unit will output a constant voltage regardless of the load resistance value it sees. The output current is determined by Ohm’s Law V = IR, and depends on the resistance of the connected load. If the load resistance becomes really small, the load will draw a current that can be excessive and large enough to cause damage. To avoid this scenario, the power supply unit should be configured such that the output current is limited to a specific maximum value. This configuration can be performed using the [Current] function on the unit. When the power supply unit outputs a constant current regardless of the configured supply voltage value and the load resistance value, the unit is said to be operating in the constant current mode. Note that the mode of operation is determined by user-specified output current limit. There is no button or menu item to toggle between these two modes.

Hand Analysis

Figure 2 – 4 DC Circuit

For the circuit in Figure 2 – 4, the voltage produced by the source is in the range of $\color{black}1V \le V_S \le 10V$ while the resistor has a resistance in the range of $\color{black}1 kΩ \le R_1 \le 10 kΩ$ . Perform the following steps.

Choose a value for V_S and R₁.
Determine the value for V_R1.
Determine the value for I_R1.
Calculate the power associated with the resistor, P_R1. Does the resistor absorb or deliver power?
Calculate the power associated with the source, P_S. Does the source absorb or deliver power?
Repeat Steps 2 to 5 with at least 4 more different V_S values while keeping R₁ unchanged.

Simulation

Simulate the circuit in Figure 2 – 4 using a circuit simulator. Determine the values for V_R1, I_R1, P_R1 and P_S. Compare all the simulation results with those determined in Hand Analysis.

Hands-on Experiment

Note that all the resistors you are going to use in the lab have a power rating of 0.25W. Please keep this information in mind.

I. Ohm’s Law and Conservation of Energy

Construct the circuit in Figure 2 – 4 using the necessary equipment and tools. Using the same V_S and R₁ values as in Hand Analysis, perform the following steps.

Measure V_R1 using a DMM.
Measure I_R1 using a DMM.
Calculate the ratio V_R1/I_R1 using the measured values. What is the ratio equivalent to?
Calculate the power associated with the resistor, P_R1. Does the resistor absorb or deliver power?
Calculate the power associated with the source, P_S. Does the source absorb or deliver power?
Is the law of conservation of power/energy obeyed?
Compile all the data in a table such as Table 1.

Table 1 Compilation of Data

	V_S	V_R1	I_R1	V_R1/I_R1	P_R1	P_S
1.
2.
3.
4.
5.

Plot V_R1 vs I_R1. What is the nature of the plot? Calculate the slope of the plot. What does the slope represent?
Compare all the measured values with those determined in Hand Analysis and Simulation.

II. Constant Voltage and Constant Current Modes in DC Power Supply

There are two major parts in this section. Both parts use the circuit in Figure 2 – 4.

For the first part, perform the following steps.

Choose R₁ = 1 kΩ.
Construct the circuit in Figure 2 – 4 using the necessary equipment and tools.
On the DC Power Supply, set the maximum output current to be 0.2A using the [Current] function.
Vary V_S from 0V to 10V. You can use any reasonable step size such as 1.0V, 0.5V, etc.
Observe the output voltage of the DC Power Supply. Does it change? What mode is the DC Power Supply operating in?

After completing the 1st part above, turn off the [Output] function on the DC Power Supply.

For the second part, perform the following steps. If you ever smell smoke while going through the process, turn off the DC Power Supply immediately.

Choose R₁ = 10 Ω.
Construct the circuit in Figure 2 – 4 using the necessary equipment and tools.
On the DC Power Supply, set the maximum output current to be 0.2A using the [Current] function.
NOTE: You MUST perform this step properly. Also, you MUST ask your ULA to double check the current setting on the power supply unit you are using before proceeding to the next step.
Turn on the [Output] function on the DC Power Supply.
Vary V_S from 0V to 5V. You can use any reasonable step size such as 1.0V, 0.5V, etc.
Observe the output voltage of the DC Power Supply. Answer the following questions.
1. Does it change?
2. When does it change? When does it remain unchanged?
3. If it remains unchanged, what mode is the power supply operating in?
4. If it does change, what mode is the power supply operating in? In this mode, what quantity remains unchanged?
5. What are the reasons for both scenarios?
When the current is 0.2A, what is the power associated with R₁? Does this value exceed the power rating?
When the current is 0.2A, what phenomenon do you observe in the experiment? If you dare, you can touch the resistor with your finger.

Test of Knowledge!

Plot P_R1 vs V_R1. What is the nature of the plot?
Plot P_R1 vs I_R1. What is the nature of the plot?
Is the power rating of a resistor important? Why?
What would happen if the power absorbed by a resistor exceeds its power rating?
When do you think you need to change the current setting on a power supply?
Why is ammeter connected in series?
Why is voltmeter connected in parallel?