An electric circuit is formed when a conductive path is created to allow electron movement. This movement of electrons, carrying an electric charge through a conductive material is called an electric current. Electrons in motion experience collisions with the lattice ions of the conductor which slows their progress. This opposition to the flow of electric current a conductor produces is called its electrical resistance (Walding, 2004). The amount of current in the circuit depends on the resistance of the material and the voltage. The force motivating electrons to move through a conductor is called voltage (V). It is a measure of potential energy per unit charge of electrons (All about circuits, 2014). Current (I) is the rate of electric charge flowing through a conductor (I=q/t where q is a quantity of charge). The relationship between current, voltage and resistance can be descried by the ohm’s law. Ohm’s law states that the current (I) flowing through a conductor is directly proportional to the voltage (V). Since resistance(R) is held constant, Ohm’s law can be written as:
Where voltage is measured in volts (v), current (I)is measured in amps (A), and the resistance is measured in ohms (Ω).Using algebra techniques, this equation can be rearranged to R = V/I. The resistance of a particular conductor depends on several factors, the geometry and the composition of the material. The longer the length (L) of the material, the greater the resistance as higher number of electron collisions occur within the material resulting in more opposition to flow. Therefore, the resistance of a conductor is directly proportional to its length. The greater the cross sectional area (A) of the material, the lower the likelihood of a collision. Therefore, the smaller the area of cross-section (A) of the conductor, the greater its resistance. The above relationships can be used to determine a formula for overall electric resistance(R);
Where is is the constant of proportionality called resistivity measured in ohmmeters (Ωm), length (L) is measured in metres (m) and the cross sectional area (A) is measured in square metres
By rearranging the above formula;
From this formula, the resistivity for any material can be defined as the resistance of the material with a unit length and a unit cross-sectional area. Electrical resistivity can also be described as a measure of how much a certain material resists flow of electrical current (Squishy Circuits Resistivity, 2014). Every material has its own resistivity which is constant. A low resistivity indicates that the material allows the movement of electrons. Conductors such as copper have low a resistivity while insulators such as glass have a high resistivity. Resistivity is an important property since it directly relates to resistance, which relates to Ohm’s law, making it a powerful tool describing the behaviour of a circuit.
Combining above formula for resistivity and ohms law (R=V/I), the following formula can be derived.
The resistivity of a material also depends on the temperature. The resistivity increases with temperature as increasing temperature causes lattice ions to vibrate with greater amplitude causing higher likelihood of electron collisions (Walding, 2004). The relationship between resistivity and temperature can be given by; ρ T = ρ0 (1 + α Δ T)
Where ρ T = conductor resistivity at T °C, ρ0 = resistivity of conductor at 0°C, α = temperature coefficient of resistivity and Δ T = change in temperature (°C) Similarly, since resistivity relates proportionally to resistance, the above equation can also be written as; RT =R0 (1 + α Δ T)
Where RT = conductor resistance at T°C and R0 = conductor resistance at 0°C.
Conductive dough can be used to determine factors affecting resistance and resistivity. The resistivity of Play dough depends on the...
References: All About Circuits,. (2014). How voltage, current, and resistance relate : Ohm 's Law - Electronics Textbook. Retrieved 2 October 2014, from http://www.allaboutcircuits.com/vol_1/chpt_2/1.html
Squishy circuits. (2012). Retrieved 9 October 2014, from http://lizastark.com/portfolio/wp-content/uploads/2012/03/Squishy.pdf
Squishy Circuits Resistivity. (2014). Retrieved 2 October 2014, from http://courseweb.stthomas.edu/apthomas/SquishyCircuits/ResistivityTesting.pdf
Walding, R., Rapkins, G., & Rossiter, G. (2004). New century senior physics (1st ed.). South Melbourne: Oxford University Press.
Resistivity. (2014). Retrieved 9 October 2014, from http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Resistivity.html
Please join StudyMode to read the full document