voltage current resistance All Scalar quantities

Ohmic Conductor Slope = Resistance If the p.d. across a length of wire is increased, the current increases proportionally. Slope = Resistance

Non-Ohmic Conductor If the p.d. across a bulb is increased, it will get hot and it’s resistance will therefore increase. The p.d. vs. current line will become steeper. Non Linear Resistance incerases with temperature

Not all materials follow Ohm’s law! Those that do are called ohmic Those that do not are called nonohmic Ohmic Nonohmic

Current and Voltage are linearly proportional

circuits

Series circuits have all their components wired so that current follows a single path through the circuit. Have you ever hooked up strings of Christmas lights? Remember how you plugged one end of a string into another string, and so on? Then you have wired circuits in series.

Series Circuits Only one path for the electrical current (water). Current flowing through each element is the same. Total voltage equals the sum of the individual voltages Total resistance equals the sum of the individual resistors

Series Circuits If R1 = 3,000, R2 = 6,000 , and R3= 9,000 and the battery supplies a voltage of 100 volts, Find: IT I1 I2 V1 V3 PT

Series Circuits If the Emf of battery is 12 V, and the 3 resistors are identical, what is the potential difference across each resistor? 12 V 0 V 3 V 4 V

In the circuit R1 is 3 , R2 is 4 , and R3 is 2 . The ammeter reading the total current leaving the battery records 1.50 A. Find: The voltage dropped over each resistor. The total resistance of the circuit? The Potential difference of the battery, VT? The power supplied by the battery?

A parallel circuit is a closed circuit, in which the current divides into two or more paths before recombining to complete the circuit. They are wired in such a way so that if one part of the circuit is broken, the whole circuit is still closed! Many complex electronic devices are wired in parallel. This allows a single source to provide power to many different components inside a device, such as a stereo system.

Parallel Circuits - There’s more than one path for the current to flow. The total current is the sum of the individual currents. The voltage across any branch is the same as the total V=V=V=V The total resistance, RT is less than the smallest one

Each new path reduces the resistance to the flow of water

The more paths for the water (current) to flow the less resistance there is to the water (current) flow.

Homes are wired in Parallel, WHY?

Power – The rate at which electric energy is being used Power – The rate at which electric energy is being used. Measured in Watts (scalar)

Current Divider Rule Current seeks the path of least resistance The current entering any number of parallel resistors divides as the inverse ratio of their ohmic value 14

Series-Parallel Circuits Most circuits are actually a combination of both series and parallel branches.

RT = R1 + R2 + R3 = 3 M + 3 M + 540 k = 6.54 x 109  VT Find: RT IT I1 I2 I3 V1 V2 V3 IT = VT / RT = 42 V / 6.54 x 109  = 6.42 x 10-9 A I1 = IT = 6.42 uA I2 = IT = 6.42 uA I3 = IT = 6.42 uA

VT RT = R1 + R2 + R3 = 880 k + 480 kW + 930 k = 2.29 M IT = VT / RT = 19 V / 2.29 x 106  = 8.29 x 10-6 A I1 = IT = 8.29 mA I2 = IT = 8.29 mA I3 = IT = 8.29 mA V1 = I1R1 = 8.29 x 10-6 A x (880 x 103)  = 7.30 V Find: RT IT I1 I2 I3 V1 V2 V3 V2 = I2R2 = 8.29 mA x 480 k = 3.98 V V3 = I3R3 = 8.29 mA x 930 k = 7.71 V

Kirchhoff’s Current Rule – Junction Rule Kirchhoff’s Voltage Rule – Loop Rule

Law of Conservation of Charge Kirchhoff's Current Law - The sum of the currents entering any node (junction) equals the sum of the currents leaving that node (junction). Law of Conservation of Charge

Stated another way Total current in = Total current out Three ammeters are located near junction P in an electric circuit as shown. If A1 reads 8.0 Amps and A2 reads 2.0 Amps, then the reading of ammeter A3 could be: 16 A 6.0 A 5.0 A 4.0 A

As an analogy, consider vehicles at a road junction As an analogy, consider vehicles at a road junction. The number of vehicles passing point 1, per minute, must be equal to the number of vehicles passing point 2 per minute plus the number of vehicles passing point 3 per minute.

Total current into any junction = Total current out of any junction

Total current into any junction = Total current out of any junction PARALLEL CIRCUIT

Total current into any junction = Total current out of any junction

Junction Rule What is the current at point P? P 5 A 8 A 2 A 2 A 3 A [CORRECT 5 ANSWER]

Junction Rule What is the current at point P? P 5 A 8 A 6 A 2 A

Kirchhoff's 2nd Law - Loop Rule - The sum of the applied potentials and the potential drops around any closed circuit loop is zero. Law of Conservation of Energy In the equation below voltage drops represented with a – sign and voltage gains with a + sign. R1 R2 v1 I - IR1 -IR2 = 0 v1 I R1 R2 = 0 v1 - IR1 -IR2 Move clockwise around circuit:

Kirchhoff's Voltage Law - The algebraic sum of the voltages around any closed path is zero. B B A C A C When you go from – to + you gain voltage When you go from + to – you loose voltage Find the difference in potential between points: A-B, B-C, C-A in both diagrams.

V = + 12 V – 8 V – 4 V = 0  Loop Rule Example Current in each resistor? Total resistance = 6  Ohm’s Law: I = V / R = 12 V / 6  = 2 A –IR = –8 V –IR = – 4 V 4  2  I 12 V Start +V = 12 V Voltage drop across resistor? V = I R V = + 12 V – 8 V – 4 V = 0 