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RC Circuits Physics 102 Professor Lee Carkner Lecture 15
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Kirchhoff’s Rules Left loop: 6 - 6I 2 = 0 6 = 6I 2 so I 2 = 1 A Right loop: 6I 2 - 6I 3 - 4I 3 = 0 Since I 2 = 1, 6 -10I 3 = 0, or 6 = 10I 3 or I 3 = 0.6 A I 1 = I 2 +I 3 I 1 = 1 + 0.6 or I 1 = 1.6 A 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 Currents are bounded by junctions Each single branch has a current Voltage Only include batteries ( ) and resistors (IR)
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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 ( V) connected to capacitor (C) The capacitor experiences potential difference of V and has stored charge of Q = C V +- + - VV C Q
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Capacitors in Parallel Potential difference across each is the same ( V) But: Q 1 = C 1 V Q 2 = C 2 V The equivalent capacitance is: C eq = C 1 + C 2 +- VV C1C1 C2C2
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Capacitors in Series Charge stored by each is the same (Q) Total V is the sum ( V = V 1 + V 2 ) Since V = Q/C: The equivalent capacitance is: 1/C eq = 1/C 1 + 1/C 2 Only the outer plates have a net charge build-up +- 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 If you add a resistor to a charged capacitor, the capacitor will discharge through it If we charge a capacitor with a resistor in the circuit, it will also take time for the capacitor to fully charge = RC 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 Q C = CV C V C = [1-e (-t/ ) ] Capacitor charges rapidly at first and then the rate of charge separation slows 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 Monday (January 26)
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Consider two resistors connected in series to a battery. One more resistor is then added in series. What happens to the current through each resistor : What happens to the (absolute value) of the voltage across each resistor? A)Increases : Increases B)Decreases : Decreases C)Increases : Decreases D)Decrease : Stay the same E)Same : Same
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Consider two resistors connected in parallel to a battery. One more resistor is then added in parallel. What happens to the current through each resistor : What happens to the (absolute value) of the voltage across each resistor? A)Increases : Increases B)Decreases : Decreases C)Increases : Decreases D)Decrease : Same E)Same : Same
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