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# Ch28 - Physics 4B Lecture Notes Chapter 28 Circuits Problem...

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Physics 4B Lecture Notes 28-1 Chapter 28 - Circuits Problem Set #7 - due: Ch 28 - 1, 9, 14, 17, 23, 38, 47, 53, 57, 66, 70, 75 Lecture Outline 1. Kirchoff's Rules 2. Resistors in Series 3. Resistors in Parallel 4. More Complex Circuits 5. Electrical Meters 6. RC Circuits In a circuit, charges move from one place to another carrying energy. These charges can be thought of as buckets that carry energy around a circuit. The battery fills the buckets. The buckets are emptied at various places around the circuit, but the buckets themselves never disappear. They return to the battery to be refilled. These basic ideas are summarized in Kirchoff's Rules and are applicable to even the most complicated circuits. 1. Kirchoff's Rules The Junction Theorem: "The current into any junction is exactly equal to the current out of the junction." This theorem is explained by the Law of Conservation of Charge. The Loop Theorem: "The sum of all the voltage drops around any loop in a circuit must be zero." This theorem is explained by The Law of Conservation of Energy and the fact that the electric force is conservative. 2. Resistors in Series I V R 1 2 R N R The loop theorem requires: V - V 1 - V 2 - L - V N = 0 V = V 1 + V 2 + L + V N Ohm's Law says: V = IR, V 1 = I 1 R 1 , V 2 = I 2 R 2 , L V N = I N R N IR = I 1 R 1 + I 2 R 2 + L + I N R N The junction theorem means that: I = I 1 = I 2 = L = I N IR = IR 1 + IR 2 + L + IR N R = R 1 + R 2 + L + R N R s = R i Resistors in Series V I R

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Physics 4B Lecture Notes 28-2 3. Resistors in Parallel I R 1 2 R N R V I 1 2 I N I The junction theorem means that: I = I 1 + I 2 + L + I N Ohm's Law says: I = V R , I 1 = V 1 R 1 , I 2 = V 2 R 2 , L I N = V N R N V R = V 1 R 1 + V 2 R 2 + L + V N R N The loop theorem requires: V - V 1 = 0, V - V 2 = 0, L V - V N = 0 V = V 1 = V 2 = L = V N So, V R = V R 1 + V R 2 + L + V R N 1 R = 1 R 1 + 1 R 2 + L + 1 R N Resistors in Parallel 1 R p = 1 R i 4. More Complex Circuits 1) Circuit elements in series have the same current, but divide up a common voltage. 2) Circuit elements in parallel have the same voltage, but divide up a common current. Many resistor circuits are just combinations of series and parallel. They can be studied using the series and parallel rules. This is called "circuit reduction." Other circuits are not combinations of series and parallel. These circuits have to be examined with Kirchoff's Rules.
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Ch28 - Physics 4B Lecture Notes Chapter 28 Circuits Problem...

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