Resistance and power

Ohm on the range or a current runs through it

Introduction

Measuring voltage across and the current through a resistor at the same time can tell you its resistance and the power it is dissipating.

Material

• two multimeters
• two AA batteries
• and a 10 ohm resistor or a flashlight bulb or one Christmas light out of a series set of 50 to 100.

To Do and Notice

Connect the resistor to the battery so that a current flows through it.

Measure the voltage across the resistor and the current through it at the same time using two different meters.

Measuring the current through and the voltage across a resistor.

Next connect two batteries in series. Measure the voltage across the resistor and the current through it.

(Optional, You could even try the same measurements for three batteries.)

If you divide the measured voltage across the resistor by the current through the resistor in the above experiments you should get nearly the same answer regardless of the number of batteries. The voltage in volts divided by the current in amps should be 10 volts per amp. This ratio is called the resistance and the ratio of volts per amp is given the name ohm. The 10 ohm resistor gives the same ratio of volts to amps for any applied voltage*.

* within reason.

What's Going On?

The greater the difference in voltage, the energy per coulomb, between the ends of the resistor, the larger the flow of current through the resistor. This linear relation between current and voltage is true for many different materials, in particular it is true for devices known as resistors. The resistor you were given claims to be a 10 ohm resistor. Was it?

Ohm's law is V = IR

where V is voltage across a circuit element
I is the current through it
and R is its resistance.

For a resistor R is a constant independent of I and V and so this equation becomes a simple proportionality. The voltage across a resistor is proportional to the current through it.

Many things behave like resistors, pieces of wire, pieces of carbon, light bulbs, toasters. However for many of these resistors, R the resistance is not constant but varies.

Ohms law does not tell you the current through non-resistors such as batteries, capacitors, diodes, transistors, or inductors.

Power

When an electrical charge flows from a place of high electrical potential to low potential it loses potential energy. In a resistor this potential energy is turned into thermal energy and the resistor gets warm. A continuous flow of charges in a current continuously releases energy. When energy is continuously converted into thermal energy we say that power is being dissipated by the resistor. Power, P, is energy per second and is measured in watts.

The power dissipated by a resistor is the product of the voltage across the resistor and the current through it.

P = VI.

In this case for a 10 ohm resistor and a 1.5 volt battery:

solve ohms law to get the current

V = IR

I = V/R = 1.5/10 = 0.15 amps

P = VI =1.5 volts x 0.15 amps = 0.225 watts.

This equation works for any circuit element as long as the voltage and current are DC, direct current.

Power and resistance are both calculated from voltage and current but power is a product , VI, and resistance is a ratio, V/I.

Measure the voltage and the current produced by a solar cell in direct sunlight. The voltage and current should be measured at the same time.

The power produced by the solar cell is P = VI, for our solar cells that are 10 cm x 10 cm the voltage was 1 volt and the current was 1 Amp. The power it produced was 1 watt.

The power in sunlight is 1 kilowatt per meter square. Our solar cell has an area of 0.01 meter^2 and so intercepts 0.01 kilowatts or 10 Watts, it produces 1 watt of power so it converts 10% of the incident energy into electric power. This is average performance for a solar cell.

Etc.

When a battery is connected to a resistor the current, (flow of positive charges) flows out of the positive terminal. This is a negative current since we defined current flowing into the positive side to be positive. The power dissipated by the battery is thus P = VI = 1.5 x -0.15 = -0.225 watts. The battery does not dissipate power it provides power. It dissipates negative power, this is rather tricky!

Resistance continued

Measure resistance using the resistance scale on your multimeter.

Material

• Multimeter with a resistance scale
• 10 ohm resistor
• you
• photo-resistor

To Do and Notice

There may be a resistance scale on your meter. This scale will allow you to measure the resistance of a circuit element directly.

A digital meter needs no adjustment. However I always check it by touching the leads of the meter together and then measuring their resistance, which should be 0.

For analog meters only.

An analog meter reads from infinite resistance on the left to zero on the right. On our meters this scale is in green.

Set the resistance scale to x 1 and measure the resistance of your 10 ohm resistor. Before you connect the meter leads to the resistor, touch the leads together making a short circuit. The resistance of this short circuit is near zero. Adjust the meter to read 0 by turning the "ohms adjust" wheel on the face of the meter.

Whenever you turn the dial to a new resistance scale you must reset the ohms adjust to read 0 for a short circuit, otherwise your readings will be meaningless.

You should measure about 10 ohms. The resistors often have resistance errors of 10%, the meter is accurate to 5%.

Measure your personal resistance. (If you are using an analog meter reset the zero on the meter.)

Depending on the sweatiness of your hands, your resistance can vary widely from under 1,000 ohms to over 500,000 ohms.

Measure the resistance of the photo-resistor Don't forget to reset the zero. Notice the effect of light on the resistance.

Use one meter to measure the resistance of a second meter set to the 5 DCV scale, try other voltage scales.

Use one meter to measure the resistance of a second meter set to the 250 ma scale.

 Scientific Explorations with Paul Doherty © 2000 2 August 2000