Online Homework 10 Solution

Transcription

1 Onle Homework Solution Phasors Explaed n this problem, you will answer some basic questions about phasors and prepare to use them the analysis o various A circuits. n parts A - consider the our phasors shown the diagram. Assume that all our phasors have the same angular requency ω. Part A At the moment t depicted the diagram, which o the ollowg statements is true? leads by Part B At the moment shown the diagram, which o the ollowg statements is true? lags 3 by Part At the moment shown the diagram, which o the ollowg statements is true? leads 4 by

2 et us now consider some basic applications o phasors to A circuits. For a resistor, the current and the voltage are always phase. For an ductor, the current lags the voltage by For a capacitor, the current leads the voltage by.. Part D onsider this diagram. et us assume that it describes a series circuit contag a resistor, a capacitor, and an ductor. The current the circuit has amplitude, as dicated the igure. Which o the ollowg choices gives the correct respective labels o the voltages across the resistor, the capacitor, and the ductor? dq cosωt dq cosωt Q sωt dt ω Q sωt cos ωt ω cosωt cosωt d dt ω sωt So the answer is ; 4 ;. cos ωt + Part E Now consider a diagram describg a parallel A circuit contag a resistor, a capacitor, and an ductor. This time, the voltage across each o these elements o the circuit is the same; on the diagram, it is represented by the vector labeled. The currents the resistor, the capacitor, and the ductor are represented respectively by which vectors? For a resistor, the current and the voltage are phase. For an ductor, the current lags the voltage by. For a capacitor, the current leads the voltage by. So the answer is ; ; 4.

3 onstructg a ow-pass Filter A series -- circuit is driven with A voltage o amplitude and requency ω. Dee out to be the amplitude o the voltage across the capacitor. The resistance o the resistor is, the capacitance o the capacitor is, and the ductance o the ductor is. Part A What is the ratio out? Express your answer te o either, ω,, and or, ω, and. ω ( ) +, out out + ( ) ( ) ( ) ω + ω Part B Which o the ollowg statements is true the large ω limit (that is, or ω >>,, )? n the large ω limite, ω >>, ω >> ω out ω Part Which o the ollowg statements is true the small limit (that is, or ω <<,, )? n the small ω limite, ω <<, ω << ω out is closed to. 3

4 4 Problem 3.99 n a certa series circuit, when the ac voltage source has a particular requency, the peak voltage across the ductor is. times greater than the peak voltage across the capacitor. Part A Determe te o the resonant requency o this circuit. Express your answer usg two signiicant igures...4 o o ω ω

5 Problem 3.85 An ductance coil draws. A dc when connected to a 48 battery. When connected to a -Hz - () source, the current drawn is 3.8 A (). Part A Determe the ductance o the coil. Express your answer usg two signiicant igures. Z Z 45 Ω.A 3.58Ω 3.8A + ( ) Z ( 3.58Ω) ( Ω) ( Hz). H Part B Determe the resistance o the coil. Express your answer usg two signiicant igures. 45 Ω.A 5

6 Problem 3.84 Part A What is the current an circuit i 5. kω,.5 µf, and the applied voltage is 3 at. Hz? Ω Hz.5 F Z Z + ( )( ) ( 5Ω) + ( Ω) 3 4.4mA 57Ω 57Ω Part B φ - tan What is the phase angle between voltage and current? tan - Ω.7 5 Ω Part What is the power dissipated by the circuit? P cosφ (.44A)( 3) cos(.7 ) 9.W Part D What are the voltmeter readgs across?.44a 5.kΩ ( )( ) Part E What are the voltmeter readgs across?.44a Ω 4.8 ( )( )