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Direct Current (DC) Circuits Introduction In this lab, we will get acquainted with various components of electrical circuits. We will learn: how to make simple circuits using a battery (or power supply), light bulbs, resistors; draw the circuit diagram; how to use color code to read the resistance of the resistor; how to use the measuring tools like a digital multimeter – DMM; how to connect the DMM to measure the resistance, voltage and current. We will learn how to simplify the circuit by replacing the circuit diagram with an equivalent one. Text reference: Young and Freedman §§ 26.1, 26.3. We will investigate the behavior of direct current (DC) electrical circuits. We will study the flow of electrical current in a circuit from the battery or power supply, through the wires, and through various combinations of light bulbs and/or resistors.

A simple electrical circuit usually has a power (energy) source such as a battery or power supply and resistors such as a light bulb or a carbon resistor. Here are the symbols for some electrical components you may see in circuit diagrams of the lab manuals of this lab course:

A closed circuit is a path along which current carriers (electrons in conductors) can flow. Current does not flow in an open circuit. A circuit in which there is a single pathway is known as a series circuit whereas a circuit that has multiple (more than one) possible paths is known as a parallel circuit. Resistors impede the flow of current in a circuit. We assume that connecting leads (conductors) have negligible resistance, while the insulators have very large resistance. Many resistors obey Ohm’s Law (V = IR), which states that the current I through a resistance R is proportional to the voltage V across the resistor. We will study Ohm’s law in the next lab class experiment. Part 1. Light Bulbs

1. Simple circuit Make a simple circuit using a battery or DC power supply, a light bulb (in its holder), and some of the connecting leads.

a) What happens to the light bulb when you close the circuit? ___________________________________________________________________

b) Draw a circuit diagram representing your circuit using the symbols from above: Try to remember how brightly the bulb is shining in step 1.

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2. Light bulbs in Series Now add a second identical bulb in series (you will need to disconnect your circuit first).

a) Draw a proper diagram representing your circuit. What do you observe about the light intensity (brightness) in each bulb compared to a single bulb in the previous step? __________________________________________________________________

b) What happens if you remove one of the light bulbs from its holder? _________________________________________________________________

3. Light bulbs in Parallel Disconnect the circuit from step 2 and add the second bulb in parallel to the first.

a) Draw a proper diagram representing your circuit. What do you observe about the light intensity in each bulb compared to a single bulb in step 1?

__________________________________________________________________ b) What happens if you remove one of the light bulbs from its holder? __________________________________________________________________

Part 2. Resistors

The Carbon Resistors A common type of resistor used in electrical circuits is made from a carbon composition in the form of a small solid cylinder with a wire lead attached to each end. The nominal resistance value is specified by a color code as it is shown for example in Figure 1.

Figure 1. Carbon resistor with 4 color band

The first three bands give the resistance in ohms in the form R = AB x 10C Ohms, where A, B, and C are integers between 0 and 9. The first band is A, the second B and the third C. The color code for the integer is:

black brown red orange yellow green blue violet grey white 0 1 2 3 4 5 6 7 8 9

The fourth band specifies the tolerance, i.e. the allowed deviation from the nominal value, according to

gold silver no band 5% 10% 20%

The resistance of the resistor shown in Figure 1 (with the color bands: A-orange, B-blue, C-brown and D-gold) according to the color code is: R = (36 x 101 ± 5%) Ohms = (360 ± 5%) Ohms = (360 ± 18) Ohms. Define the resistances of the resistors R1; R2; R3 you have at your station using the color code and compare them with the direct measured values using DMM (digital multimeter) as an ohmmeter (the dial - at Ω (Ohm) position).

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Resistors connected in series and in parallel are shown in Figure 2.

Figure 2a) Resistors in series

Figure 2b) Resistors in parallel

1. Simple circuit

Make a circuit by replacing the light bulb in step 1 in Part 1 with the resistor R1. Use the DMMs to measure the voltage across the resistor and the current passing through it. In order to measure the voltage across a resistor the DMM (voltmeter option - the dial is on DC V position) must be connected in parallel to the resistor by connecting the two probes on either side of the resistor. In order to measure the current through a resistor, the DMM (ammeter option - the dial is on DC A position) must be connected in series so that it is part of the current path. Show your connection to your TA before closing the switch. In Figure 3 the voltmeter is connected in parallel to the light bulb, while the ammeter is connected in series.

Figure 3. Connecting the voltmeter and ammeter in circuit.

In both cases connect the red terminal R of the DMM to the high potential point (which is closer to the positive terminal of the power source) and the COM (black) terminal B of the DMM to the low potential point. Otherwise you will see a negative reading on the DMM display.

2. Resistors in series Measure the resistances of two resistors R1 and R2 using DMM’s as an ohmmeter. Connect two resistors in series and make a circuit by connecting them with the power source.

a) Draw a proper diagram representing your new circuit. Measure the current in circuit, current through each resistor and voltage drop on each resistor.

b) What can you say about the currents and voltages? c) Do the current values through the resistors differ? Explain why? d) Do the values of the voltage drop across the resistors differ? e) Are these relations Vj = Ij·Rj correct for each resistor? f) How is the sum of the voltage drops across the resistors related to the voltage of the

battery or the power supply?

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On the basis of your measurements can you conclude that the total resistance Rt of two resistors R1 and R2 connected in series is given by the equation: Rt = R1 + R2?

Hint: Vt = V1 + V2 or It·Rt = I1·R1 + I2·R2. Measure the effective resistance Rt using the DMM and compare with the sum of the measured R1 and R2. Does Rt = R1 + R2?

3. Resistors in parallel Connect two resistors in parallel and make a circuit with them connected with the power source.

a) Draw a proper diagram representing your new circuit. Measure the total current in the circuit, the current through each resistor (you will need to disconnect one end of the resistors to connect the DMM as an ammeter), and the voltage drop on each resistor.

b) What can you say about the currents and voltages? c) Do the current values through the resistors differ? d) Do the values of the voltage drop across the resistors differ? e) Are these relations Vj = Ij·Rj correct for each resistor? f) How is the sum of the currents trough the resistors related to the total current in the

circuit? On the basis of your measurements can you conclude that the total resistance Rt of two resistors R1 and R2 connected in parallel is given by the equation: 1/Rt = 1/R1 + 1/R2?

Hint: It = I1 + I2 or Vt/Rt = V1/R1 + V2/R2. Measure the effective resistance Rt using the DMM. Does 1/Rt = 1/R1 + 1/R2. Part 3 Connect the resistors as shown in Figure 4 (combination of series and parallel connection). Calculate the total resistances RAB for the diagram shown below. Show your calculations.

a)

equivalent to

b)

Figure 4. The equivalent diagrams.

On the diagram b) the resistor R1 is connected in series with R23 which is the effective resistance of two resistors R2 and R3 connected in parallel on diagram a). Measure the total resistance RAB using the DMM as an ohmmeter and compare your calculated and measured values of total resistances. Self-assessment questions: 1. How do we connect an ammeter in a circuit (in parallel or in series)? 2. How do we connect a voltmeter in a circuit (in parallel or in series)? 3. How can you calculate the equivalent resistance for resistors connected in series? 4. How can you calculate the equivalent resistance for resistors connected in parallel?

Part 1. Light Bulbs

Part 2. Resistors