# Useful Formulas and How to solve them for the Extra Exam

## These are questions originaly taken from the Advanced Exam pool, most of them are on the current extra exam.

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What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 14.25 MHz and a Q of 187?

BW = f / Q, so the bandwidth is 14,250,00 / 187 = 76,203 HZ

What is the Q of a parallel R-L-C circuit if the resonant frequency is 14.225 MHz, L is 3.5 microhenrys and R is 10 kilohms?

Q = R / X for a parallel circuit where X is the circuit reactance and R is the resistance X for inductance is 2 pi f L where f = frequency and L = inductance.
Q = 10,000 / (2 * 3.1416 * 14,225,000* 0.0000035) = 31.96

What is the value of capacitance (C) in a series R-L-C circuit if the circuit resonant frequency is 14.25 MHz and L is 2.84 microhenrys?

C=1/4*pi^2 * f^2 * L 1/4*pi^2*14,250,000^2*.00000284 = .0000000000439239 or 44 picofarads

What is the Q of a parallel R-L-C circuit if the resonant frequency is 3.625 MHz, L is 3 microhenrys and R is 2.2 kilohms?

Q=R/2*pi*F*L
2200/2*pi*(3,625,000*.000003)=32.1968 or rounding up to a Q of 32

What is the resonant frequency of a parallel R-L-C circuit if R is 4.7 kilohms, L is 2 microhenrys and C is 15 picofarads?

f = 1 / ( 2 pi sqrt(L * C) = 29.06 MHZ

What is the resonant frequency of a series R-L-C circuit if R is 47 ohms, L is 40 microhenrys and C is 200 picofarads?

If Q is at all large, Fr = 1/(6.28 * (the square root of L*C)) 1/(6.28 * (sqrt (.00004 * .000000000,2)))=17.80 Mhz

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?

For power, 1dB = 1.26, 3dB = 2, 6dB = 4, and 10 dB = 10, the effective gain is 1 dB, so the answer is 252 watts erp.

Here is another way. 1db power ratio is 1.2589:1

1.2589*200=251.78W

How many turns will be required to produce a 5-microhenry inductor using a powdered-iron toroidal core that has an inductance index (A sub L) value of 40?

(1000*sqrt(L/(A sub L))= N

Here is another way

Sqrt (L*(Al*10-9)) = N
Sqrt (5*10-6/40*10-9) = 11.18T
round down to 11 turns.

What is the phase angle between the voltage across and the current through a series R-L-C circuit if Xc is 250 ohms, R is 1 kilohm, and XL is 500ohms?

Ø = tan-1((Xl -Xc)/R)

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