# Series and Parallel Circuits

DC Experiment 2

### Background

The total or equivalent resistance of a series circuit, denoted as RT, equals to the sum of all resistors connected along the path. In Figure 2.1, the three resistor are connected in series therefore its total resistance is determined as:

If all resistors have same value R, the above equation simply turns into:

Where N is the number of resistors in this series circuit.

While resistors are connected in parallel, it can be identified as all terminals on each side connect to the same voltage level as shown in Figure 2.2. Mathematically, the total resistance RT for a parallel circuit is calculated as:

If there are only two resistors in parallel, it is more convenient to use:

In this experiment, we will implement simple series and parallel resistor circuits on a breadboard and verify the above equation using experimental approaches.

### Procedure

**Part I: Series Circuit**

Use multi-meter (VEGO) to measure each individual 1kΞ© resistor and record the measured values as R1, R2 and R3.

Using the formula for series resistance, calculate RT using the measured resistance. Record the RT in Table 1 column 1.

In Figure 2.3, connect R1, R2 and R3 in series. Set VEGO to position [Ξ©] and connect the probes to the end terminals of the series circuit. Record the measured resistance in Table 2.1 column 2.

The total resistance measured directly by the multi-meter should equal to the mathematical summation of each individual resistance.

As shown in Figure 2.8, measure the voltage across the three resistors and the total current flowing out from the power source. Record results in Table 2.2 column 3 and 4.

Measure the voltage across the resistors and the current through the resistors (see Figure 2.5). Record the measured voltage and current in Table 2.1 column 3 and 4 respectively.

Use correct multi-meter modes when measuring voltage and current.

Calculate the total resistance using Ohmβs Law based on the measured voltage and current. Record the calculated resistance in Table 2.1 column 5.

**Part II: Parallel circuit**

Using the given formula, calculate the total resistance of the three 1kΞ© resistors connected in parallel:

also, record this calculated result in Table 2.2 column 1.

Connect the three 1.0 kΞ© resistors in parallel as seen in Figure 2.6. Measure the equivalent resistance and record this value in Table 2.2 column 2.

Build the circuit on breadboard as shown in Figure 2.7. Set power supply voltage to 5V.

As shown in Figure 2.8, measure the voltage across the three resistors and the total current flowing out from the power source. Record results in Table 2.2 column 3 and 4.

Calculate the total resistance using Ohmβs Law based on the measurements. Record the calculated resistance in Table 2.2 column 5.

### Exercises

In Table 2.1 and Table 2.2, are the total resistances determined by different approaches close enough? (Compare column 1, 2 and 5 in each Table)

If the power supply is still connected while measuring the total resistance with a multi-meter, is the approach valid? For example, in Figure 2.4, measure the total resistance while power supply is turned on and connected.

Find an expression for the total resistance RT of the circuit shown below. Then determine RT when R1 = R2 = 1kΞ©, R 3 = 500Ξ© and R4 = 2kΞ©.

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