Electricity: Voltage, Current, and Ohm's Law

ELECTRICITY: VOLTAGE, CURRENT, and OHM'S LAW

OBJECTIVE: To study the relation between voltage and current (Ohm's Law), to use Ohm's Law to investigate resistance measurements, and to investigate the factors upon which the resistance of a conductor and sets of conductors depends.

TERMINOLOGY: meters conductor insulator circuit symbols: current (I) voltage (V) resistance (R) power (P) units: amps [A] volts [V] ohms [] watts [W]

THEORY: Current is defined as the flow of electricity (flow of charges). It is measured in amps [A]. Voltage is defined as the energy per charge at a particular position and is measured in volts [V]. Current tends to flow from a place of high voltage to a place of low voltage - just like water tends to flow from a place of higher elevation to a place of lower elevation. (Hence, elevation in water flow is analogous to voltage in current flow.) Resistance is simply how much the material resists the flow of charges and is measured in ohms []. (In our water analogy, water flowing through large pipes encounters very little resistance, while water flowing through a sponge or through sand encounters a higher resistance.) A voltage source (such as a battery or a power supply) is like a water pump: a water pump can move water from a lower place to a higher place; the voltage source moves the charge from a place of low voltage (negative terminal) to a place of high voltage (positive terminal). A circuit is simply a path for the charges to flow from the high voltage position to the low voltage position, just like pipes or rivers can form a "circuit" for water flow.

The individual circuit elements are connected in such a way that the current flows through them, usually giving up energy in the process. As the charges give up energy, the potential energy of the charges (and hence the voltage) will decrease as they traverse the circuit. OHM'S LAW states that for most common conductors the potential difference (V) across the conductor is proportional to the current (I) that flows through the conductor:

V = I R . (1)

The resistance is then simply the constant of proportionality and is a measure of how hard it is to force the current through the conductor: the bigger the resistance, the more voltage is needed to force a certain amount of current; or alternately, the bigger the resistance, the less current will flow through the resistance for a certain voltage.

(NOTE: Although the formula should read V = IR, we often measure voltage like we measure height: from some common reference level we label as 0, and hence V and V become the same.)

In this experiment we will use the law to calculate the resistance of certain conductors, after measuring the current and the potential difference. Since both the ammeter (for current measurements) and the voltmeter (for potential difference measurements) have some resistance, there will be certain errors in the measurements. Corrections would have to be made for this in very accurate work. Electricity: Voltage, Current, and Ohm's Law 2

There are two basic ways of connecting components into a circuit: series and parallel. In SERIES, the same current must flow through each component. In PARALLEL, the current will divide and different amounts will flow through the different components. The current in a series circuit is the same throughout, so an ammeter is always connected in series. A voltmeter measures the voltage difference between two points in a circuit, or across a particular part of a circuit, and this means that a voltmeter is always connected in parallel.

In using D.C. instruments, care must be taken to connect them up with the proper polarity. The terminal marked (+) should always be connected to the positive terminal of the power supply and the terminal marked (-) to the negative terminal. They need not be connected directly, but you should be able to trace back to the proper terminal. On many instruments only one terminal is marked, and it is understood that the other is the opposite polarity. On meters with more than one scale, the number on the terminal refers to the MAXIMUM value that can be measured on that scale.

METHOD: In Part One, the current in a resistor is varied by changing the applied voltage. The currents and the corresponding voltages are measured. A voltage-current curve is plotted and the slope of a straight line fitted to the points yields a value of a resistance which can be compared to the known value.

In Part Two, we use a length of wire as our resistor. The potential difference across various lengths of resistance wire are measured while the current is kept constant. A graph of resistance versus length (which should yield a straight line) will illustrate the dependence of resistance on length of conducting wire.

In Part Three, the resistance of several coils of wire of various sizes and materials are measured by the voltmeter-ammeter method. From this data, the variation of resistance with length, cross-sectional area and material is noted.

In Part Four, two light bulbs are used as resistors and the resistance of the different combinations of the bulbs is analyzed.

*CAUTION: The power supply output should be turned down between readings to minimize heating of the resistors. Heat causes the resistance to increase and this could decrease the accuracy of your results.

Part 1. Ohm's Law: V = IR

PROCEDURE: 1. Connect the apparatus as shown in Fig. 1, using the 10 ohm resistor for R. Although this

resistor is stamped 10 , it will not be exactly 10 ohms when measured. Resistors are guaranteed accurate only within a certain percent (10% in this case) which is usually indicated on the resistor in some way. The power supply (PS) has a control so that by rotating it the voltage across the resistor (and hence the current through the resistor) can be varied from zero to some maximum value. Electricity: Voltage, Current, and Ohm's Law 3 2. Adjust the voltage control on the PS so that about 0.5 A runs through the resistor. Then take readings of voltage and current at about 0.1 A intervals as the current is decreased from 0.5 A to zero.

+ + PS R V - A - - +

Fig. 1

REPORT: 1. Display your data (voltage vs. current) in tabular form. 2. Plot a graph of voltage (ordinate or vertical axis) and current (abscissa or horizontal axis). 3. Compute the slope of the best straight line through the points. Use a point on the line near the top and one near the bottom to calculate the slope. (Recall that the slope is the change in vertical quantity divided by the change in the horizontal quantity.)

4. Compute the percent difference between the slope and the nominal value of 10  for the resistor. Is it less than 10%?

Part 2. Resistance vs Length

PROCEDURE: 1. Connect the slide wire to the power supply as shown in Fig. 2. Adjust the power supply voltage so that a current of 0.5 Amps or less flows through the circuit.

2. Record the voltages and currents for lengths, ℓ, of the wire of 20, 40, 60, 80, and 100 cm. Simply move one of the alligator clips of the voltmeter to change the length.

 wire

- + V + PS - + - A

Fig. 2

REPORT: 1. Report your data (voltage vs. current for each length) in tabular form. 2. Calculate the resistances of the various lengths of wire (using V=IR). 3. Plot a graph of resistance against length. As best as you can, fit a straight line to the points. Electricity: Voltage, Current, and Ohm's Law 4 4. Describe or express in some way the relation between the resistance of a conductor and its length as illustrated by your graph.

Part 3. Resistance: R = ℓ/A

The board in this part has five coils of wires. The coils on the board are labeled according to their size (determined by the gauge number which is related to the diameter of the wire), material (described by , the resistivity of the material), and the length of wire (ℓ) connected between the pairs of terminals.

A #28 gauge wire has a diameter of 0.032 cm and a #22 gauge wire has one of 0.064 cm. Recall that the cross-sectional area of a cylindrical object, such as a wire, is given by A = r2 where the radius r is half of the diameter. The resistivity of copper is  = 1.72x10-6 -cm. That of German silver is  = 33x10-6 -cm.

PROCEDURE:

1. Connect the apparatus as shown in Fig. 3.

resistor coils . 1 . 2 . 3 . 4 . 5 .

+ - + V PS + - - A

Fig. 3

2. Measure the current and voltage across coil #1. Calculate the resistance for this coil of wire using Ohm's law.

3. Repeat this procedure for coils #2, 3, 4, and 5. Be sure to write down the specifications of the wires connected between each pair of terminals.

REPORT: 1. Report your data (V and I for each coil) in tabular form. 2. For wires of the same material and cross-sectional area, is your relation between resistance and length in part 2 confirmed? 3. For wires of the same material and length, is the resistance bigger for the thicker or the thinner wire? How would you describe the dependence of resistance on area: is R A or is R 1/A? 4. For coils 1 and 5 the length and thickness are the same but the material is different. Does the material affect the resistance? This is described by a quantity called the resistivity for which the symbol  (Rho) is used. Taken together, the resistance of a conductor of Electricity: Voltage, Current, and Ohm's Law 5

cross-sectional area A and length ℓ is given by the equation R =  ℓ / A. Do your results support this?

Part 4. Resistance in Series and Parallel

PROCEDURE: WARNING: Do NOT go above 5 volts across any one light bulb or you may burn the bulb out!

1. Using your voltmeter and your ammeter, determine the resistance of each light bulb twice: once when the filament is relatively cool (measure I when V = 1 volt and note brightness of bulb) and again when the filament is very hot (measure I when V = 5 volts and note

brightness of bulb). In the case of a light bulb, the filament is designed to get very hot (

5000 F) so that it glows when 5 volts is placed across it. Determine whether the resistance of the light bulb (essentially that of the filament) stays constant as the temperature goes up.

2. Replace the one light bulb with two light bulbs connected in series. (In other words, make the current flow through both resistors - do not give it a choice). Now set the voltage of the PS to 5 volts and note both the current and the brightness of both bulbs. Are they the same brightness as when you placed five volts across each separately? Is the same current going through each as when you had 5 volts across them separately? Is the current indicated by the ammeter the same as the current flowing through light bulb #1 only, #2 only, both, or the sum of the currents through #1 + #2 ? What do you have to do to the voltage to make both light bulbs bright? What happens to the current when you do this (particularly, compare the current to that for the single bright light bulb of step 1) ?

3. Unhook the two light bulbs and re-hook them in parallel. (In other words, give the current a choice of flowing either through light bulb #1 or light bulb #2.) Now set the voltage of the PS to 5 volts, measure the current, and note how bright each light bulb is. Are they the same brightness as when you placed five volts across each separately? Is the same current going though each as when you had 5 volts across them separately? Is the current indicated by the ammeter the same as the current flowing through light bulb #1 only, #2 only, both, or the sum of the currents through #1 + #2 ?

REPORT: 1. Answer the questions asked in the procedure part above.

2. By placing more resistance in the circuit in a series fashion, does the overall (effective) resistance increase, decrease, or stay the same. Is this consistent with the results of part 2

which indicated that R  ℓ ?

3. By placing more resistance in the circuit in a parallel fashion, does the overall (effective) resistance increase, decrease, or stay the same. Is this consistent with the results of part 3

which indicated that R  (1/Area) ?

4. Since voltage is defined as energy per charge and current is charge per time, voltage times current gives energy per time or POWER. Power is measured in Watts [W], so 1 VA = 1W. a) For having both bulbs bright, which circuit (parallel or series) takes more power? b) For the same voltage, which circuit generated the most light from the light bulbs? c) In your household wiring, do you connect appliances in series or parallel to the outlet?