Series and Parallel Resistor Circuits



Series and Parallel Resistor Circuits Activity

When working with circuits Ohm’s Law is a valuable tool in evaluating for the current, resistance and voltage. Ohm’s Law states that the voltage or emf, å, supplied to a circuit is equal to the current in the circuit times the resistance of the circuit.

V = IR

Series circuits consist of resistors that are connected one after another. The total current in the circuit flows through each consecutive resistor. The total resistance in the circuit is the sum of each of all of the resistors in the series.

Itotal = I1 = I2 = I3 …

Reff = R1 + R2 + R3 …

Vtotal = V1 + V2 + V3 …

Figure 1:

R1 R1 R2 R1 R2 R3

A A A

Parallel circuits are composed of resistors that are connected parallel to each other as rungs on a ladder are parallel to each other. The effective resistance is reduced below the smallest resistor since each resistor offers another path for the electrons to pass through. The effective resistance is given by the following equation.

1 1 1 1

Rtotal = R1 + R2 + R3 …

Since the total current has different paths through which to travel the sum of the current in each path is equal to the total current.

Itotal = I1 + I2 + I3 …

The electric potential drop or voltage drop across each resistor in the parallel set up are equal. This is due to the fact that the electric potential is measured from the same place and thus has to be the same.

Vtotal = V1 = V2 = V3

Figure 2:

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A. Series Circuits Procedure:

1. Set up the single resistor in series with the ammeter across the voltage source as shown in figure 3. Next connect the voltmeter across the resistor to measure the voltage drop across it. Adjust the volt sources so that the voltage across the resistor is approximately 6 volts. Record the printed value of the resistor, voltage across the resistor and amperage through the resistor. For this first resistor use Ohm’s Law to calculate the resistance of the resistor using the measured values of voltage and amperage.

Printed resistor value, R1 = ____________, Voltage reading, V1 = _____________,

Amperage reading, I1 = __________, Calculated value for resistor, R1 ____________.

Figure 3: Single Resistor Figure 4: Two Resistors in Series

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2. Now wire in a second resistor in series with the first resistor as shown in Figure 4. Connect the volt meter across both resistors and adjust the voltage source so that the volt meter read approximately 6 volts. Make readings and record the values for the total current or amperage, Itotal, voltage across the combined resistors, Vtotal, and then voltage across each individual resistor, V1, V2. Record the printed values for both resistors, R1 and R2.

Printed resistor value, R1 = ____________, Printed resistor value, R2 = ____________,

Voltage reading, V1 = _____________, Voltage reading, V2 = _____________,

Voltage reading, Vtotal = _____________, Amperage reading, Itotal = __________,

Now calculate the effective resistance using the printed values of the resistors and compare that with the calculate value for the total resistance using the Ohm’s Law and the measured values of Vtotal and Itotal.

Calculated effective resistance for the circuit using the printed resistor values, Reff ____________

Calculated resistance using the Vtotal and Itotal, Reff calculated ___________

Now calculate the total voltage using V1 and V2 and compare that with the measured value for Vtotal.

Calculate Vtotal ____________

3. Now wire in a third resistor in series with the first two resistors. Connect the volt meter across all three resistors and adjust the voltage source so that the volt meter read approximately 6 volts. Make readings and record the values for the total current or amperage, Itotal, voltage across the combined resistors, Vtotal, and then voltage across each individual resistor, V1, V2, V3. Record the printed values for all resistors, R1, R2, and R3.

Printed resistor value, R1 = ____________, Printed resistor value, R2 = ____________,

Printed resistor value, R2 = ____________, Voltage reading, V1 = _____________,

Voltage reading, V2 = _____________, Voltage reading, V3 = _____________,

Voltage reading, Vtotal = _____________, Amperage reading, Itotal = __________,

Now calculate the effective resistance using the printed values of the resistors and compare that with the calculate value for the total resistance using the Ohm’s Law and the measured values of Vtotal and Itotal.

Calculated effective resistance for the circuit using the printed resistor values, Reff ____________

Calculated resistance using the Vtotal and Itotal, Reff calculated ___________

Now calculate the total voltage using V1, V2, and V3 and compare that with the measured value for Vtotal.

Calculate Vtotal ____________

B. Parallel Circuits Procedure:

1. Now set up two resistors in parallel as shown in Figure 5. The resistors should be connect to the same junction on the left and to another junction on the right. Make readings and record the values for the total current or amperage, Itotal, current in resistor 1 and 2 or I1 and I2, voltage across the combined resistors, Vtotal, and then voltage across each individual resistor, V1, V2. Record the printed values for both resistors, R1 and R2.

Figure 5: Two resistors in parallel Figure 6: Three resistors in parallel

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Printed resistor value, R1 = ____________, Printed resistor value, R2 = ____________,

Voltage reading, V1 = _____________, Voltage reading, V2 = _____________,

Voltage reading, Vtotal = _____________, Amperage reading, Itotal = __________,

Amperage in resistor 1, I1 = ______________, Amperage in resistor 2, I2 = ______________

Now calculate the effective resistance using the printed values of the resistors and compare that with the calculate value for the total resistance using the Ohm’s Law and the measured values of Vtotal and Itotal.

Calculated effective resistance for the circuit using the printed resistor values, Reff ____________

Calculated resistance using the Vtotal and Itotal, Reff calculated ___________

Now calculate the total current using I1 and I2 and compare that with the measured value for Itotal.

Calculate Itotal ____________

2. Now set up three resistors in parallel as shown in Figure 6. The resistors should be connected to the same junction on the left and to another junction on the right. Make readings and record the values for the total current or amperage, Itotal, current in resistor 1, 2 and 3 or I1, I2 and I3, voltage across the combined resistors, Vtotal, and then voltage across each individual resistor, V1, V2, and V3. Record the printed values for all three resistors, R1, R2, and R3.

Printed resistor value, R1 = ____________, Printed resistor value, R2 = ____________,

Printed resistor value, R3 = _____________, Voltage reading, V1 = _____________,

Voltage reading, V2 = _____________, Voltage reading, V3,

Voltage reading, Vtotal = _____________, Amperage reading, Itotal = __________,

Amperage in resistor 1, I1 = ______________, Amperage in resistor 2, I2 = ______________

and Amperage in resistor 3 I3 = __________________

Now calculate the effective resistance using the printed values of the resistors and compare that with the calculate value for the total resistance using the Ohm’s Law and the measured values of Vtotal and Itotal.

Calculated effective resistance for the circuit using the printed resistor values, Reff ____________

Calculated resistance using the Vtotal and Itotal, Reff calculated ___________

Now calculate the total current using I1, I2, and I3 and compare that with the measured value for Itotal.

Calculate Itotal ____________

Questions:

1. State and explain the relationships for current, voltage and resistance in a series circuit. Show the equations for these relationships and explain how the represent the relationships.

2. State and explain the relationships for current, voltage and resistance in a parallel circuit. Show the equations for these relationships and explain how the represent the relationships.

3. Explain how Ohms law applies series and parallel circuits.

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