Lecture19_Kim

Lecture19_Kim - Lecture 19-1 PHYS241 Question 1 November 1,...

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Lecture 19-1 PHYS241 – Question 1 – November 1, 2011 All the inductors below are identical and so are all the resistors . Which circuit have the longest time constant? A B D C
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Lecture 19-2 Alternating Current (1) Now we consider a single loop circuit containing a capacitor , an inductor , a resistor , and a source of emf or different combinations of them This source of emf is capable of producing a time varying voltage where is the angular frequency and V max is the amplitude or maximum value of the emf Notation: instantaneous values are denoted by small letters ( v , i ) , amplitudes by capital letters ( V , I ) max sin emf v V t
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Lecture 19-3 To begin our analysis of RLC circuits, let’s start with a circuit containing only a resistor and a source of time-varying emf as shown to the right Applying Kirchhoff’s loop rule to this circuit we get where v R is the voltage drop across the resistor Substituting into our expression for the emf as a function of time, we get Remembering Ohm’s Law, V = iR , we get Circuit with Resistor (1) 0 (t)= emf R R v v v v sin RR v V t sin sin vV i t I t  max sin v V t sin i I t R R V I R
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Lecture 19-4 Thus we can relate the current and the voltage in the regsiste by We can represent the time varying current by a phasor I R and the time-varying voltage by a phasor V R as shown below Phase difference is 0 Circuit with Resistor (2) RR v i R sin v V t sin R v i I t R  sin v V t sin i I t v R (t) and i(t) in phase R R V I R
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Lecture 19-5 Mean vs Root-Mean-Square 2 0.7 1 0 2 7 rms pea peak k I i I I sin 0 peak i I t  0 0 1.41 2 peak rms II I  2 2 2 2 1 sin 2 peak peak i I t I Circuit with Resistor (3)
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Lecture 19-6 Root-Mean-Square Values 22 1 2 pe a ak s v rm I R I R P 
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Lecture19_Kim - Lecture 19-1 PHYS241 Question 1 November 1,...

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