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RC Circuits Physics 102 Professor Lee Carkner Lecture 16

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Kirchhoff’s Rules Left loop: 6 - 6I 2 = 0 Right loop: 6I 2 - 6I 3 - 4I 3 = 0 Since I 2 = 1, 6 -10I 3 = 0, or 6 = 10I 3 or I 3 = I 1 = I 2 +I 3 I 1 = 1 + 0.6 or I 1 = Voltage: For battery V = 6 V, for 6 , V = 6I 2 = 6 V, for 2nd 6 , V = 6I 3 = 3.6 V, for 4 , V = 4I 3 = 2.4V + - V = 6 V 4 6 I1I1 I3I3 I2I2

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Kirchhoff Tips Current Each single branch has a current Voltage Only include batteries and resistors

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Capacitance Remember that a capacitor stores charge: The value of C depends on its physical properties: Note that capacitance does not depend on V How can we combine capacitors in circuits?

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Simple Circuit Battery removes electrons from the left side and transfers them to the right +- + - VV C Q

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Capacitors in Parallel Total stored charge is the sum (Q = Q 1 + Q 2 ) But: Q 1 = Q 2 = Q = The equivalent capacitance is: C eq = C 1 + C 2 +- VV C1C1 C2C2

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Capacitors in Series Equivalent capacitor also has a charge of Q Total V is the sum ( V = V 1 + V 2 ) Q/C eq = Q/C 1 + Q/C 2 1/C eq = 1/C 1 + 1/C 2 +- VV C1C1 C2C2 + -- +

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Capacitors in Circuits Remember series and parallel rules extend to any number of capacitors Keep simplifying until you find the equivalent capacitance for the whole circuit

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Resistors and Capacitors After a certain amount of time, all the energy in the capacitor will go into heating the resistor A capacitor C paired with a resistor R will have a time constant ( ) This is the time to charge a capacitor to about 63% of the final value

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Charging a Capacitor

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Time Curve

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Charge Over Time If we charge a capacitor by connecting it to a battery of voltage , the charge and voltage on the capacitor is: Q C = CV C As you charge the capacitor you increase the repulsive force which makes adding more charge harder

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Next Time Read: 20.1, 20.4 Homework: Ch 19 P 31, 50, Ch 20 P 10, 11 Quiz 2 next Friday

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