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Calculating resonant frequency from L and C.
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E5A25 (A)
What is the resonant frequency [F0] of a series RLC circuit if R is 47 ohms, L is 3 microhenrys and C is 15 picofarads?
A. 23.7 MHz
B. 23.7 kHz
C. 35.4 kHz
D. 35.4 MHz
Resonant frequency F0 = 1000 MHz / 2pi * sqrt (L mH * C pF) for SERIES circuits. All questions specify series circuits, no need to consider parallel.
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Calculating Phase angle from RLC
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E5D01 (A)
What is the phase angle between the voltage across and the current through a
series R-L-C circuit if XC is 25 ohms, R is 100 ohms, and XL is 100 ohms?
A. 36.9 degrees with the voltage leading the current
B. 53.1 degrees with the voltage lagging the current
C. 36.9 degrees with the voltage lagging the current
D. 53.1 degrees with the voltage leading the current
Phase angle = arctan ( (Inductive reactance - Capacitive reactance) /
Resistance). If result is positive, voltage leads, if negative, voltage lags
current. Easier to draw it than calculate it: triangle,
resistance on the x-axis, inductive reactance XL minus capacitive reactance
XC on the y-axis. phase angle is the angle subtended by the hypotanuse and
the x-axis. If the triangle points north, voltage leads; if south,
current leads.
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Calculating RC Time Constant
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E5B08 (C)
What is the time constant of a circuit having a 220-microfarad capacitor in
series with a 470-kilohm resistor?
A. 47 seconds
B. 80 seconds
C. 103 seconds
D. 220 seconds
The time required to charge a capacitor to 63.2 percent of full charge or
to discharge it to 36.8 percent of its initial voltage is known as the
TIME CONSTANT (TC) of the circuit. Time/charge curve is geometric;
two time constants = 86.5% in charge, 13.5% discharge.
The value of the time constant in seconds is equal to the product of the
circuit resistance in ohms and capacitance in farads. For questions on
the test, it's easier to first convert to megohms (10^6) and microfarads
(10^-6)than ohms and farads.
470 kilohm = .47 megohm
.47 megohm * 220uF = 103 sec.
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Calculating Circuit Q from resonant freq., R and L
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E5G15 (A)
What is the Q of a parallel RLC circuit if the resonant frequency [F0]is
7.125 MHz, L is 10.1 microhenrys and R is 100 ohms?
A. 0.221
B. 4.52
C. 0.00452
D. 22.1
Q for a PARALLEL RLC is R / (2pi * F0 * L) For a SERIES RLC circuit it
is the inverse (1/Q). Microhenrys cancel megahertz, no need to scale these.
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Caluclating half-power bandwidth from resonant freq. and circuit Q
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E5A12 (A)
What is the half-power bandwidth B of a parallel resonant circuit that has a
resonant frequency F0 of 1.8 MHz and a Q of 95?
A. 18.9 kHz
B. 1.89 kHz
C. 189 Hz
D. 58.7 kHz
Q = F0 / B, whether series or parallel. Hence B = F0/Q
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Estimating Effective Radiated Power (ERP)
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E5H10 (B)
What is the effective radiated power of a repeater station with 200 watts
transmitter power output, 2-dB feed line loss, 2.8-dB duplexer loss, 1.2-dB
circulator loss and 7-dBd antenna gain?
A. 159 watts
B. 252 watts
C. 632 watts
D. 63.2 watts
ERP can be estimated closely enough by adding the db losses and gains, and
figuring that for every 3db net gain, ERP doubles. So if you have a 100W
feed and a net gain of 3db, ERP is 200W; 6db gain = 400W.
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RECTANGULAR COORDINATES
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E5C10 (A)
In rectangular coordinates, what is the impedance of a network comprised
of a
10-microhenry inductor in series with a 40-ohm resistor at 500 MHz?
A. 40 + j31,400
B. 40 - j31,400
C. 31,400 + j40
D. 31,400 - j40
Resistance is the real component of the imaginary number, impeadance is the
imaginary component. Inductance is positive, capacitance negative.
Regardless of the magnitude of the j value, only A can be correct.
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POLAR COORDINATES
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Polar coordinates plot the phase angle and magnitude of the inductance.
Phase angle can be calculated as we saw earlier from RLC,
phase angle = atan ( (XL-XC) / R). C is negative, L is positive.
The cartesian trig method discussed above works fine for these as well.
E5E01 (B)
In polar coordinates, what is the impedance of a network comprised of a
100-ohm-
reactance inductor in series with a 100-ohm resistor?
A. 121 ohms, /__35_degrees__
B. 141 ohms, /__45_degrees__
C. 161 ohms, /__55_degrees__
D. 181 ohms, /__65_degrees__
This is a 1R-1L-sqr(2X) isoscolese right triangle in the positive quadrant.
E5E02 (D)
In polar coordinates, what is the impedance of a network comprised of a
100-ohm-
reactance inductor, a 100-ohm-reactance capacitor, and a 100-ohm
resistor all
connected in series?
A. 100 ohms, /__90_degrees__
B. 10 ohms, /__0_degrees__
C. 10 ohms, /__100_degrees__
D. 100 ohms, /__0_degrees__
This is a 100 ohm vector along the resistance axis. XL-XC=0, which
divided by anything is still 0.
E5E03 (A)
In polar coordinates, what is the impedance of a network comprised of a
300-ohm-
reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm
resistor, all
connected in series?
A. 500 ohms, /__37_degrees__
B. 400 ohms, /__27_degrees__
C. 300 ohms, /__17_degrees__
D. 200 ohms, /__10_degrees__
This is a 3-4-5 triangle, 37 deg. positive (inductive).
E5E04 (D)
In polar coordinates, what is the impedance of a network comprised of a
400-ohm-
reactance capacitor in series with a 300-ohm resistor?
A. 240 ohms, /__36.9_degrees__
B. 240 ohms, /__-36.9_degrees__
C. 500 ohms, /__53.1_degrees__
D. 500 ohms, /__-53.1_degrees__
This is a 3-4-5 triangle, 37 deg. negative (capacitive).
E5E06 (D)
In polar coordinates, what is the impedance of a network comprised of a
100-ohm-
reactance capacitor in series with a 100-ohm resistor?
A. 121 ohms, /__-25_degrees__
B. 191 ohms, /__-85_degrees__
C. 161 ohms, /__-65_degrees__
D. 141 ohms, /__-45_degrees__
This is a 1R-1L-sqr(2X) isoscolese right triangle in the negative quadrant.
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Plotting Addmittance in millisiemens
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E5E17 (B)
In polar coordinates, what is the impedance of a circuit that has an
admittance
of 7.09 millisiemens at 45 degrees?
A. 5.03 x 10(-5) ohms, /__45_degrees__
B. 141 ohms, /__-45_degrees__
C. 19,900 ohms, /__-45_degrees__
D. 141 ohms, /__45_degrees__
Siemens (Mohs), the measure of admittance, are the reciprocal of Ohms,
the measure of resistance or impeadence.
Thus 1 / N millisiemens / 1000 millisiemens per moh = ohms.