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Question #1

 

A circuit consists of three resistors in series, with values 200 W, 100 W and 60 W.

This series circuit is connected across a battery with an output voltage of 36 volts.

 

a.  (4) What is the current flowing in this series circuit?

 

b.  (4) What is the power dissipated in the 100 Ω resistor in the circuit described in (a) above.

 

c.   (4) The battery is replaced by a sine wave source with a frequency of 60.0 Hz and a peak voltage of 50.9 volts.  What is the rms current flowing in the 100Ω resistor?

 

d.   (4) In the circuit described in part (c) above, how much power is dissipated in the 100 W resistor?

 

e.  (5) A telephone handset has a resistance of 600 W.  It is connected to the local telephone exchange at a distance of 5 km by a twisted pair.  Each wire in the pair has a resistance of 100 W per km.

 

The telephone exchange has a 48.0 V battery that is connected to the twisted pair through a

 400 W resistor.  What is the DC current through the handset when it is off-hook?

 

 

 

Question #2

 

 A circuit consists of a sine wave signal generator and a reactive component (L or C).

The output of the generator is a sine wave with a peak amplitude of 8.88 volts at a frequency of          10.0 kHz. (Be sure you know the correct units for your capacitor, inductor.)

 

a.  (4) The generator is connected to an inductor with L = 10.0 mH.  What is the rms current flowing in the inductor?

 

b.  (4) The generator is connected to a capacitor with C = 0.0250 mF.  What is the rms current

     flowing in the capacitor?

 

c.  (4) What is the power dissipated in the capacitor in part (b) above?

 

 

 

 

 

 

 

 

Question #3 

 

 a.  (4) A FM radio station transmits at a frequency of 89.9 MHz.  A radio receiver has a telescoping rod (as seen on most portable FM radio receivers) antenna that is a quarter wavelength long monopole. What is the optimum length of this antenna to receive the F M station, correct to the nearest cm?

 

b.  (5) AM radio stations vary the amplitude of the transmitted signal in order to convey the program information. The signal has the form of v(t) = A cos(2πft + ϕ).  When there is no modulation (i.e. the amplitude is constant), the radio station delivers 1000 watts into a 50Ω antenna (i.e. the antenna acts as if it is a 50Ω resistor) and it has a frequency of 1.5 MHz.  Fill in the appropriate values for the v(t) that appears at the antenna: A, f and ϕ.

 

v(t) =

 

c.  (4) Typical AM radio stations limit the highest frequency transmitted in the program material to 5000 Hz.

 

Is this adequate for voice transmission?  Explain.

 

Is this adequate for music transmission?  Explain.

 

Question #4

 

(5) A signal generator outputs a unipolar square wave with a period of 0.50 ms with an amplitude of 2.0 V.  The output of the generator is passed through an ideal band pass filter that has a pass band that extends from 1.0 kHz to 9.0 kHz (i.e. it passes all frequencies between 1.0 kHz and 9.0 kHz and rejects everything else).  List the peak amplitude (in volts) and frequency (in kHz) of each wave that is present at the filter output.

 

 

Question #5

 

A signal generator outputs a sine wave signal with a frequency of 2000 Hz and an rms voltage of 1.0 V.  The output of the signal generator is connected to a 50 Ω resistor.

 

a.  (5) What is the power dissipated in the 50 W resistor in watts, in dBW, and in dBm?

 

b.  (5) An amplifier with a gain of 100  (i.e. the output power is 100 times greater than the input power) over the frequency range 0 Hz to 10 kHz is placed in the circuit between the signal generator and the resistor.  What is the power dissipated in the 50 W resistor in watts, dBW, and dBm now?  Do you calculation in dB units and then convert to watts.

 

c.  (5) An attenuator (an attenuator REDUCES the power level by the specified dB)  with a fixed attenuation of 6.0 dB over the frequency range 0 Hz to 10 kHz is placed in the circuit between the amplifier and the resistor.  What is the power dissipated in the 50 W resistor in watts and dBm now?

 

 

Question #6. 

 

An audio signal has a bandwidth that extends from 100 Hz to 10 kHz. It is passed through a low pass filter that has a cutoff of 10 kHz but it is not an ideal filter.  The signal is sampled to create a PAM signal and then digitized by a linear 10 bit analog to digital converter (ADC).  The digital signal is transmitted as a serial bit stream to a distant location where it is converted to parallel words and input to a digital to analog converter (DAC).  The output of the DAC is passed through a low pass filter. 

 

a.  (4) The sampling rate is to be 1.2 times the Nyquist rate.  What is the sampling frequency?

 

 

b.  (4) What is the bit rate at the output of the ADC?

 

c.  (4) What is the best cut off frequency for the low pass filter at the receiving end of the link?  You may assume that the filter is ideal.

 

d.  (4) What is the quantization SNR at the output of thelow pass filter?

 

 

 

Question #7

 

A 1μF capacitor is charged through a 100kΩ resistor through a switch from a 12V battery.  Initially the capacitor is discharged.  See Figure A.15 in the text.

 

a.  (4) What is the time constant of this circuit? (Be sure the units are correct)

 

 

b.  (5) The switch is closed and the capacitor starts to charge. 

What is the capacitor voltage

just at the instant the witch is closed?           

 

after t = ½ a time constant

 

after t = 1 time constant

 

after t = 2 time constants

 

after t = 5 time constants

 

 

The 1μF  capacitor is charged to 12V.  Now the switch and the resistor are in series connected across the capacitor.  The switch is closed and the capacitor starts to discharge.

 

c.  (4) Does this change the circuit time constant?   

 

 

d.  (5) What is the capacitor voltage

just at the instant the witch is closed?           

 

After t = ½ a time constant

 

After t = 1 time constant

 

After t = 2 time constants

 

After t = 5 time constants

 

 

10 pt of extra credit:  Plot of the capacitor voltage vs time.  Use your spreadsheet plotting function.  Plot capacitor voltage on the y axis and time x axis in time constants, i.e. 1, 2, 3, 4, 5 time constants for both the charge and the discharge.  You will have two plots.  Plots must be properly label

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