phys lab report

3/3/2021 UNT PHYS 2240 Lab ENG_PHYS_2 E&M_FALL_2020 - Alymjan Rejepov/Experiment 4: Series and Parallel Circuits/Background Informat…

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UNT PHYS 2240 Lab ENG_PHYS_2 E&M_FALL_2020 - Alymjan Rejepov/Experiment 4: Series and Parallel Circuits/Background Information

Introduction

Content LA Thirteen - Jun 10, 2020, 11:28 PM CDT

The purpose of this experiment is to help the student understand series and parallel circuits, how to calculate their equivalent resistance, and how to construct them in the laboratory. The resistance of four circuits will be determined both theoretically and experimentally. The experimental resistance will be calculated by measuring both the voltage and current of the constructed circuits. The behavior of light bulbs connected in series and parallel will also be examined.

Content LA Thirteen - Jun 10, 2020, 11:28 PM CDT

Theory

Content LA Thirteen - Jun 10, 2020, 11:28 PM CDT

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Calculating Equivalent Resistance

A resistor generally means a device that obeys Ohm’s Law (many devices do not) and has a resistance R.

Ohm’s Law: V = IR Equation 1

Two (or more) resistors can be connected in series (as in circuit diagram 1), or in parallel (as in circuit diagram 2). Resistors can also be connected in a series/parallel circuit as shown in circuit diagrams 3 & 4. An equivalent resistor is a single resistor that could replace a more complex circuit and produce the same total current when the same total voltage is applied. This is shown in Figures 1 and 2. For a series circuit, the resistances are additive:

Req = R1 + R2 Equation 2

where Req is the equivalent resistance.

Figure 1: Resistors in Series

For a parallel circuit, the resistances add as reciprocals

Remember, when adding fractions, they must have like denominators!

We must multiply each fraction so that they have common denominators.

So we get that

If we take the reciprocal of both sides we obtain another expression for calculating equivalent resistance in parallel circuits.

Content LA Thirteen - Jun 11, 2020, 11:05 PM CDT

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A more complex circuit like Circuit Diagram 3 can be handled by combining R1 and R2 into an equivalent resistance with Equation 4. That equivalent

resistance is then put in series with R3 and equation 2 is used to find the equivalent resistance for the whole circuit. Circuit Diagram 4 can be handled

in a similar manner.

In series circuits the current is the same through each resistor, but the voltage drop across each resistor may be different. Likewise, in a parallel circuit the voltage drop across each resistor is the same, but the current through each resistor may be different.

Power

A simple understanding of power will help the student understand what is physically happening in this experiment. Power is the rate at which work is done for a system. Electrical power is defined as:

P = IV Equation 5

Where P is the power measured in watts, I is the current in amperes, and V is the voltage drop across the device measured in volts. It is useful to consider power in terms of current and resistance. Remember that Ohm’s law relates voltage to current and resistance. If this is plugged into equation 4, another way of writing power is developed. This is only true for devices that obey Ohm’s law!

P = IV =I(IR) = I2R Equation 6

R is the resistance measured in ohms. Power is directly proportional to resistance and the current squared. If two devices have the same resistance, but device 1 has twice as much current running through it compared to device 2, device 1 will have 4 times the power.