Series, Parallel and Combinations Circuits

Course: Section: Name(s): Instructor: Date:

Introduction and Objectives: In this experiment the circuit characteristics of resistors when connected in series, parallel or mixed combination will be investigated. Ohm’s law is still applicable in this case.

Theory: Resistors can be connected in Series, Parallel or mixed combination. Depending on the type of resistor combination, the circuit might have different values of voltage and/or current across different part of the circuit. Below we discuss types of resistor combination and the resulting circuit properties in detail: a) Series Combination: Resistors are said to be connected in series when they are connected in a line (head to tail) so that the current does not have any other alternate path to go through [Figure 1].Current: Since there is no alternate path, the same current passes through all the resistors: I = I1 = I2 = I3.

Voltage: The voltage drop across each resistor is not equal to V, but the sum of the voltage drops:V = V1 + V2 + V3

Resistance: The equivalent resistance of the three resistors is: Req = R1 + R2 + R3

b) Parallel: Resistors are said to be connected in series when all the “heads” are connected together as are all the “tails” [Figure 2].

Voltage: the voltage drops across all the resistors are the same and equal to the voltage (V) of the source: V = V1 = V2 = V3

R3R2R1

AV

Figure 1: Resistors in Series

V

R3

R2

R1

Figure 2: Resistors in Parallel

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Current: the current (I) from the source gets divided among the resistors: I = I1 + I2 + I3.

Resistance: The equivalent resistance of the resistors can be calculated by the formula:1/Req = 1/R1 + 1/R2 + 1/R3

Equipment Required: Three resistors (eg. 100 Ω, 150 Ω and 470 Ω), ammeter, voltmeter or multi-meter, circuit board, connecting wires, power supply.

Lab Procedures: Before you begin your lab, read the color codes of the three resistors and record them in Table1.

Table 1: Resistor R1 R2 R3

Color code on resistor (bands seen)Magnitude of resistance (corresponding Ω value from color code chart)

I) Series Circuit:1) Connect the three resistors and the voltage source into the series circuit as shown in Figure 1 above. Use a voltage of about 1.5 volts for your experiments.

Three resistors in series

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2) Use the ammeter (connected into the circuit) to read the current in the circuit across each resistor. The current should be the same throughout the circuit. Record these values in the first row of Table 2.

Figure 3: Reminder on how to connect Ammeter and Voltmeter

3) Connect a voltmeter across the individual resistors and then across the combination of resistors. Record your values in the first row of Table 2. 4) Calculate R1, R2 and R3 using (R = V/I, Ohms = Volts/Amp). Record these values in the first row of Table 3.5) Calculate Req using Req = R1 + R2 + R3. Record this in row 1, column 4 of Table 3. 6) Calculate Req using the known values of the resistors using their color codes (add individual resistances). Record this in row 1, column 5 of Table 3. 7) Record all the resistances in Ohms (Ω).How to measure current across a resistor

How to measure current across a resistor

Ammeter connected to resistor

Remove one end of the resistor and connect it to the positive terminal of the ammeter

Negative lead from ammeter goes back to circuit

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II) Parallel Circuit:1) Connect the same three resistors into the parallel circuit as shown in Figure 2 above.2) Set your power supply to deliver a voltage of about 1.5 volts. Read the voltage across each resistor. This should be the same as the total voltage (from the source). Now insert the ammeter into each resistor branch and record the current for all three branches. Also record the total current in the circuit.3) Record your readings in the second row of Table 2.4) Calculate all the individual resistances (R1, R2, R3) and the equivalent resistance (Req ) using your data in Table 2 and record your results in Table 3 (in the second row of the parallel circuit).5) Calculate the theoretical value of the equivalent resistance using your data in Table 1, for the resistors in parallel: 1/Req = 1/R1 + 1/R2 + 1/R3. Record this value in row 2, column 5 of Table 3.

III) Combination Circuit:1) Connect the same three resistors into the series and parallel circuits (combination circuit) shown below:

Resistors in series and parallel

V

R3

R2

R1

Three resistors in parallel

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2) Set your power supply to deliver a voltage of about 1.5 volts. 3) Read and record the currents and voltages in all the branches.4) Calculate the resistances using your measurements (R = V/I, Ohms = Volts/Amp)5) Calculate the equivalent resistance.

Data Tables:

Table 2Circuit Vtot V1 V2 V3 I1 I2 I3

SeriesParallelCombination

Table 3Calculate the resistances using your measurements from table 1 and the formula: R = V/I. Enter your answers in the table 3.

Circuit R1 (experimental)

R2 (experimental)

R3 (experimental)

Req (experimental)

Req (theory) Using Table 1

SeriesParallelCombination

Combination circuit

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Calculations:

Show your formulas and calculations for Theoretical Equivalent Resistance:

i) Series:

ii) Parallel:

iii) Combination:

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Questions:

1. In which circuit is the current the same in each element?

2. In which circuit are all the potential drops the same?

3. In which circuit is the total voltage the sum of all the individual voltages?

4. In which circuit is the equivalent resistance less than each individual resistance?

5. In which circuit is the equivalent resistance greater than each individual resistance?

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