Circuit Theory NCEA AS2.6 Text Chapters:

Electric Current A flow of electric charge is called an electric current. Current I is measured by the rate at which electric charge flows Current = charge/time I = Q/t Unit: Ampere (Amp) A So 1A=1Cs -1 Current direction is defined as the direction of positive charge flow.

Voltage Current will only flow continuously if there is a closed circuit. To get the charges to flow, they need to experience the force of an electric field. To set up a field, we apply a voltage or potential difference to the circuit.

Voltage A voltage V is a measure of the difference in potential energy of the charge between two points in a circuit. Voltage=Energy/ChargeV=E/Q So 1V=1JC -1 A voltage can be positive or negative. ie energy gain or energy loss.

Resistance All materials have a certain amount of electrical resistance R. This inhibits the flow of charge and uses up the charge’s energy. A material with very high R is called an insulator. A material with very low R is called a conductor. Resistance is measured in Ohms 

Resistance Resistance is directly proportional to Length. Longer = more resistance…… Resistance is inversely proportional to the cross-sectional area. Thicker = less resistance Resistance is directly proportional to the resistivity  of the material In summary: R=L  /A

Ohm’s Law Current, voltage and resistance are linked by Ohm’s Law: V=IR This applies only to conductors that have constant resistance. Examples of non-Ohmic conductors include diodes, lamps, thermistors and LDRs.

Series and Parallel If the components are linked one after the other they are in series. If they are linked alongside each other they are in parallel Series Parallel

Meters Ammeters measure current. Connected in series so that all the charge flows through them Connected in series so that all the charge flows through them low R so that they do not use up the energy of the charge. low R so that they do not use up the energy of the charge. BE CAREFUL – Ammeters are easy to damage. BE CAREFUL – Ammeters are easy to damage. Voltmeters measure voltage. Connected in parallel with the component they are measuring the voltage drop/gain across. Connected in parallel with the component they are measuring the voltage drop/gain across. High R so that they do not draw too much current away from the circuit. High R so that they do not draw too much current away from the circuit.

Combining Resistors When connected in series, the total resistance R T is the sum of the individual resistors: R T =R 1 +R 2 +R 3 …. R T =R 1 +R 2 +R 3 …. This has the effect of increasing the resistance of the circuit. This has the effect of increasing the resistance of the circuit. When connected in parallel, the total resistance is found by adding reciprocals…. 1/R T = 1/R 1 +1/R 2 +1/R 3 …. 1/R T = 1/R 1 +1/R 2 +1/R 3 …. This has the effect of reducing the total resistance of the circuit This has the effect of reducing the total resistance of the circuit

Circuit Theory Series Circuits: Current must be the same everywhere as there is only one path for electrons to take. Current must be the same everywhere as there is only one path for electrons to take. Voltage must be shared by all resistors Voltage must be shared by all resistors 4.5V 9.0V

Circuit Theory Parallel Circuits: Current can split to go down either pathway Current can split to go down either pathway Each resistor gets all the energy the charge is carrying so voltage across each is the same Each resistor gets all the energy the charge is carrying so voltage across each is the same Parallel 9V 4A2A

Summary ParallelSeries VoltageSameShared CurrentSharedSame Resistance 1/R T = 1/R 1 +1/R 2 +1/R 3 …. R T =R 1 +R 2 + R 3 …

Internal Resistance Even components like batteries and meters have resistance. This means that even though a battery is supposed to supply 9V for example, what you get across it’s terminals may be less if you try and draw a large current from it. The battery’s resistance uses some of the energy.

Potential Dividers Used to control voltage of parts of a circuit Works great as long as the load resistor is large compared to divider resistors. (Why??) V out = R 2 /(R 1 +R 2 )xV source VsVs R1R1 R2R2 V out

Power Power = Energy/time However V=E/Q & I=Q/t so combining them: P = VxI = E/QxQ/t = E/t P = VxI = E/QxQ/t = E/t Power is measured in Watts W By substituting Ohm’s Law into the power equation, it can also be written as: P=I 2 R or P=V 2 /R P=I 2 R or P=V 2 /R This shows that the higher the current the more power dissipated as heat.

Electrical safety 1mA is the maximum safe current the human body can take. 100mA probably fatal R(dry skin)=10k  If 10V applied, I=1mA (safe) If 10V applied, I=1mA (safe) If 240V applied I=24mA (hmmm) If 240V applied I=24mA (hmmm) R (wet skin)=1.2k  If 240V applied I=200mA (R.I.P) If 240V applied I=200mA (R.I.P)