SPH3U: Electricity Kirchhoff's Laws & Resistors

Circuits Review  Label the following as a Parallel Circuit or a Series Circuit. Label all the parts of each circuit. A +- V +-

Loads  Any component or device in a circuit that transforms electric potential energy into some other form of energy, causing an electric potential drop, is called a load. Two loads in the above diagrams are: the light bulb and the resistor.

Series and Parallel Circuits To understand how series circuits and parallel circuits work, we need to answer two questions: 1. When electrons have several loads to pass through, what controls the amount of electric potential energy they will lose at each load? 2. When electrons can follow several possible paths, what controls the number of charges that will take each path?

Series and Parallel Circuits To answer these questions, we need to talk about two important laws for electric circuits:

Law of Conservation of Energy As electrons move through an electric circuit they gain energy in sources and lose energy in loads, but the total energy gained in one trip through a circuit is equal to the total energy lost.

Law of Conservation of Charge Electric charge is neither created nor lost in an electric circuit, nor does it accumulate at any point in the circuit.

Kirchhoff's Laws A German physicist, Gustav Robert Kirchhoff ( ) performed experiments and was able to describe these conservation laws as they apply to electric circuits:

Kirchhoff's Laws Kirchhoff's Voltage Law (KVL) Around any complete path through an electric circuit, the sum of the increases in electric potential is equal to the sum of the decreases in electric potential. V total = V 1 + V 2 + V 3 + … + V n (in a series circuit) V total = V 1 = V 2 = V 3 = … = V n (in a parallel circuit)

Kirchhoff's Laws Kirchhoff's Current Law (KCL) At any junction point in an electric circuit, the total electric current into the junction is equal to the total electric current out. I total = I 1 = I 2 = I 3 =…= I n (in a series circuit) I total = I 1 + I 2 + I 3 +…+ I n (in a parallel circuit)

Kirchhoff's Laws These relationships are very important to understand the transfer of electrical energy in a circuit. They provide the basis for electric circuit analysis in this course.

Example Problem 1 Calculate the potential difference, V2, in the circuit shown in the figure below.

Example Problem 1 Calculate the potential difference, V 2, in the circuit shown in the figure below.

Example Problem 2 Calculate the electric current, I 3, in the circuit shown in the figure below.

Example Problem 2 Calculate the electric current, I 3, in the circuit shown in the figure below. Since this is a parallel circuit, I total = I 1 +I 2 +I 3 Therefore, I 3 = 6A

Resistance When charges pass through a material or device, they experience an opposition or resistance to their flow. Remember: Current is the number of electrons moving in the same direction past a certain point in one second. The symbol for electric current is I.

Resistance Increasing the resistance in a circuit decreases the current that flows. In 1827 a man named Georg Simon Ohm discovered that current and the potential difference V are directly proportional.

Resistance This means I α V  The more current you have (the more coulombs per second going past a point), the greater the electrical energy. This is summarized as OHM’s LAW  The potential difference V across a conductor is directly proportional to the current that flows in the conductor.

Resistance We can also write this as an equation if we put in a constant. V = cR, where c is a constant  But this property depends on the resistance… so we will make the constant c = R, and define R as the resistance.

Ohm’s Law V = IR or Note: V is measured in volts I is measured in amperes. …. So R is measured in: 1 Ω is the electric resistance of a conductor that has a current of 1 A through it when the potential difference across it is 1 V. 1 Ω = 1 V/A Ohm’s Law

Example Problem 3 What is the potential difference across a toaster of resistance 13.8 Ω when the current through it is 8.7 A?

Example Problem 3 What is the potential difference across a toaster of resistance 13.8 Ω when the current through it is 8.7 A?

Resistors in Series Resistors are put in many electronic machines to reduce the current and protect the machine parts.

Equivalent Resistors Look at the diagram. It shows a circuit with three resistors connected in series. +- R 2 = 5 Ω R 3 = 10 Ω R 1 = 6 Ω

Equivalent Resistors We would like to find the equivalent resistor  We would like to take out all the resistors and put in just one ‘super- resistor’ that would make the circuit behave in the exact same way. Remember from Kirchhoff's Law: V total = V 1 + V 2 + V 3 + ….

Equivalent Resistors Use Ohm’s Law to substitute V = IR: I total R total = I 1 R 1 + I 2 R 2 + ….

Equivalent Resistors But we also know from Kirchhoff's law that for a series circuit I total = I 1 = I 2 = I 3 = …… So, we get I total R total = I total (R 1 + R 2 + R 3 +…) Therefore, R total = (R 1 + R 2 + R 3 + …) This means, looking back at our original question, that the equivalent resistor to the diagram is R 1 + R 2 + R 3 = ( ) Ω = 21Ω

Example Problem 4 What is the equivalent resistor in a series circuit containing a 16 Ω light bulb, a 27Ω heater, and a 12 Ω motor?

Example Problem 4 What is the equivalent resistor in a series circuit containing a 16 Ω light bulb, a 27Ω heater, and a 12 Ω motor?

Resistance in Parallel We can use the same approach to find the equivalent resistance of several resistors connected in parallel. Remember from Kirchhoff's Law: I total = I 1 + I 2 + I 3 +…

Resistance in Parallel Use Ohm’s Law to substitute I = V/R: But we also know from Kirchhoff’s law that for a parallel circuit V total = V 1 = V 2 = V 3 = …

Resistance in Parallel So, we get Therefore,

Homework Read sections 11.6 & 11.7 in your text. Complete the following questions: Pg. 522 # 1-2 Pg. 526 # 2, 4, 6. Pg. 530 # 5 (a-d)