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### simple network presentation

1. 1. RESISTORS IN SERIES, PARALLEL, AND SIMPLE NETWORKS Physics II
2. 2. RESISTORS IN SERIES <ul><li>Series – components arranged to provide a single conducting path for current </li></ul><ul><li>Cardinal Rules for a Series Circuit: </li></ul><ul><ul><li>The current in all parts of a series circuit has the same magnitude. </li></ul></ul><ul><ul><li>The sum of all the separate drops in potential around a series circuit is equal to the applied emf. </li></ul></ul><ul><ul><li>The total resistance in a series circuit is equal to the sum of all the separate resistances. </li></ul></ul>
3. 3. RESISTORS IN SERIES - EXAMPLE <ul><li>The circuit to the left has an emf of 12 V. If R1 = 6 Ω , R2 = 8 Ω , and R3 = 10 Ω , calculate: </li></ul><ul><li>R T </li></ul><ul><li>The current through each resistor </li></ul><ul><li>The voltage drop across each resistor. </li></ul>
4. 4. RESISTORS IN SERIES <ul><li>Notice again, the sum of the voltage drops across the circuit is equal to the emf of the circuit. In other words, there is 12 V of potential, and that drops to zero when you reach the battery again. </li></ul><ul><li>Gustav Kirchhoff stated this in another way in his 2 nd Law – the algebraic sum of all the changes in potential occurring around the complete circuit is equal to zero . In other words, Energy is conserved! </li></ul>
5. 5. RESISTANCES IN PARALLEL <ul><li>Parallel – a circuit in which two or more components are connected across two common points in the circuit to provide separate conducing paths. </li></ul><ul><li>Cardinal Rules of Parallel Circuits: </li></ul><ul><ul><li>The total current in a parallel circuit is equal to the sum of the currents in the separate branches. </li></ul></ul><ul><ul><li>The potential difference across all branches of a parallel circuit must have the same magnitude </li></ul></ul><ul><ul><li>The reciprocal of the total resistance is equal to the sum of the reciprocals of the separate resistances in parallel. </li></ul></ul>
6. 6. RESISTORS IN PARALLEL - EXAMPLE <ul><li>If the emf of the battery of this circuit equals 12 V, and R1 = 5 Ω , R2 = 10 Ω , and R3 = 8 Ω , calculate: </li></ul><ul><li>R T </li></ul><ul><li>I T </li></ul><ul><li>I 1 , I 2 , and I 3 </li></ul><ul><li>The voltage drop across each resistor. </li></ul>
7. 7. RESISTANCES IN PARALLEL <ul><li>Notice again that the current into the juncture is equal to the currents in each branch. </li></ul><ul><li>In other words, Kirchhoff’s 1 st Law applies to parallel circuits: the algebraic sum of the currents at any circuit juncture is equal to zero. </li></ul><ul><li>In other words, charge is conserved! </li></ul>
8. 8. RESISTORS IN SIMPLE NETWORKS <ul><li>Practical circuits are more complicated than these simple examples – you have combinations of series and parallel resistors, and might have different sources of emfs. </li></ul><ul><li>A complex network needs to be reduced stepwise to a simple equivalent resistance. </li></ul><ul><li>To do this, you want to separate different parts of the circuit! </li></ul>
9. 9. RESISTORS IN SIMPLE NETWORKS - EXAMPLE <ul><li>Find the following: </li></ul><ul><li>R T </li></ul><ul><li>I T </li></ul><ul><li>The current though each resistor </li></ul><ul><li>The voltage drop across each resistor </li></ul>
10. 10. THE LAWS OF RESISTANCE <ul><li>In the case of pure metals and most metallic alloys, the resistance of the material is proportional to the temperature. </li></ul><ul><li>The resistance of a uniform conductor is proportional to the length of the conductor. (in cm) </li></ul><ul><li>The resistance of a uniform conductor is inversely proportional to its cross-sectional area. (usually in square cm) </li></ul><ul><li>The resistance of a given conductor depends on the material of which it is made. A given material has a constant associated with its resistance – the constant is called resistivity constant ,  and usually has the units of Ω -cm. </li></ul>