### Experiment 2

#### Ohm's Law

Objective:

The objective of this experiment is to verify Ohm's law.

Equipment:

A few ceramic resistors (100Ω - 300Ω), a rheostat (variable resistor), a dc power source, 2 multi-meters, a calculator, and a few connecting wires with alligator clips

Theory:

Ohm's law states that the ratio of the voltage across a resistor to the current through that resistor is a constant called the "electric resistance, R of that resistor.

V is in volts and I in amps.  That makes unit of R to be "volt per amp." that is called "Ohm."  The symbol for "Ohm" is "Ω" pronounced "omega."

Procedure:

 Note:  If you have never used a multi-meter to measure electric resistance, current, and potential difference, refer to the end portion of this manual for a detailed description on such measurements.

Arrange a circuit as shown in Fig. 1.  Note that the voltmeter reads the voltage across R, and the ammeter reads the current through R.  If you change the rheostat setting, the total resistance will change, and with a relatively fixed voltage (supplied by the battery), the current I will change.  The change in the current I through R causes the voltage across R to change; however, you will observe that the V/I ratio remains constant.

Figure 1

Move the rheostat slider to five different positions, and at each position, read the voltage across and current through R from the meters and record their values in the following table:

 Rheostat Position Current  I  (A) Voltage V (volts) R = V/I  (Ω) 1 2 3 4 5 Mean R:

Plot the results on a V versus I graph.  Draw a straight line that best fits the data.  Determine the slope of the line.  Also, find the mean value of the resistance R in the last column of the above chart.  The slope of the graph must match the mean value of R.  Why?

Data:

Given

Typical values to be used are:

Vbat. = (5 - 10) Volts.

= (100 - 150) Ω.

Rv = (0 - 90 ) Ω.

Measured:

Record the measured values of I and V at each rheostat setting in the table.

Calculations:

For each rheostat setting, calculate R = V/I.   The mean value of V/I gives us the experimental (measured) value for R.   The slope of the graph of V versus I provides the same information as well.

This value must be compared with the accepted value of R that is measured directly by an ohm-meter.

Comparison of the Results:

Calculate a % error on R.

Conclusion: To be explained by students.

Discussion:  To be explained by students.

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Multi-meters:

Multi-meters can at least read potential difference (voltage), current, and electric resistance.  In addition, multi-meters may be capable of other functions, but for now, we will concentrate on the measurement of these three physical quantities.  In this experiment, we will learn how to read a multi-meter when it is on the following settings:

-         Resistance setting

-         dc Voltage setting (Battery)

-         ac Voltage setting (City electric outlet)

-         dc Current setting (Battery)

-         ac Current setting (City electric outlet current type)

Note that "dc" stands for direct current (a current that does not change direction), and "ac" stands for alternating current (a current that keeps changing direction).

(a)  Resistance Measurement:

Place the meter on its highest Resistance setting.  Then connect each of its terminals to one end of a ceramic resistor.  For reading a resistance, it does not matter which terminal is connected to which end of the resistor.   If no reading is displayed, lower the setting until a reading is obtained.  It is possible to read a value on more than one setting in the ohm range.  Use the one with the best number of significant figures.  Repeat this procedure until all resistances are measured and the values of the resistances are written down.  Next, use a Color Codes Chart to determine the resistances of the same resistors.  Compare the results for each resistor and calculate a percent difference using the following formula:

(b)    DC Voltage Measurement:

To read a fixed voltage such as that across the terminals of a battery, a voltmeter must be set in an appropriate range in its "--V" settings.  This is a symbol for dc voltage.  Set the multi-meter at the appropriate safe range for measuring the voltage across the dc power source.  The appropriate safe range is determined by looking at the maximum voltage a power supply or a battery can offer.  For example, a 12 V car battery can supply at the most 14 volts and the appropriate range on the meter is the 20V setting.  If we choose the 2V setting of the meter, the meter will show a "1" indicating "out of range voltage."  It can damage the meter.

Connect the terminals of the power source to the appropriate terminals of the multi-meter (Positive to Positive, and Negative to Negative).  The Negative on the meter is also labeled as "COM" for common.  Increase and decrease the voltage of the source, and observe how the readings on its meter as well as those on the multi-meter change.  Try to adjust the voltage, as read from the meter on the power supply, to 2V, 4V, and 7V, as closely as you can.  Each time, read the same voltages from the multi-meter.  For each, calculate a percent difference by using equation (2).

(c)   AC Voltage Measurement:

Under the supervision of your lab instructor, set the multi-meter to its 200V ac setting.  The ac setting on the multi-meter is shown as "~V ".  Make sure that one wire is connected to COM and the other to POS on the multi-meter.  Next, insert the wires (with needle-like metal endings) into a city electrical outlet.  For ac measurements, it does not matter which wire goes into which terminal.  Write down the ac voltage you read.  If you see some fluctuations, it is because of the changes in demand by all users.  Users keep turning off and on different electric devices.

(d)   Direct Current Measurement:

Measuring current is different from measuring voltage.  For voltage, we say "the voltage across a power source or a resistor, but for current, we say " the current through a source or a resistor."  Suppose you want to measure the voltage across R1 in the following circuit:

Figure 2

To do this, you need to first set the multi-meter to the appropriate dc voltage setting and then connect its terminals to points a and b (across the resistor) as shown in Fig. 3.

Figure 3

We say that the voltmeter is connected across the resistor.

In order to measure the current, the circuit must be opened (disconnected) first (Fig. 4), and then the multi-meter must be placed inside the circuit as shown in Fig. 5.  Note that an appropriate (safe) current setting must be selected because the multi-meter is now being used as an ammeter.  First, the circuit is opened.

Figure 4

Next, the ammeter is placed into the circuit.

Figure 5

Now that you have paid attention to the way a multi-meter measures current, connect the power source (while off), to a 100Ω resistor, and a multi-meter (set at an appropriate current setting) in series as shown above Fig. 5.

The appropriate current setting can be determined by estimating the amount of current, in amperes, that goes through R1.   Simply divide the voltage (5V) by the resistance (100Ω).  The result is 0.05 A.  Multiply by 1000 to convert to milli-amps (mA).  You get 50mA.   Any range on the multi-meter that can measure more that 50mA will be safe.  Some multi-meters may have 100mA or 200mA settings.   Choose the appropriate one.  Once you are sure of the correct milli-amps setting, and also sure that the power source gives the desired voltage, turn on the power source and read the current displayed by the ammeter.  If the displayed current is close to 50mA, you have done it right.

Calculate a percent error between the current you read from the ammeter (Measured value) and the calculated value (Accepted value) of 50mA.  The formula for percent error is

It is important to always remind yourself of the way current is to be measured.  The circuit or branch through which the current is to be measured must be opened first, and then the ammeter must be inserted into that branch.

(e)   Alternating Current Measurement:

Some multi-meters are capable of measuring alternating currents and some are not.  If they are designed to do so, the method of using them for this purpose is similar to measuring a dc current.  However, "clamp ammeters" are used to measure ac currents.  AC current measurement is not included in this experiment.