Appreciate chegg but I rate the questions so if you dont know it, dont answer. A

Question

Appreciate chegg but I rate the questions so if you dont know it, dont answer.

A: A capacitor is connected to a 11 kHz oscillator that produces an rms voltage of 9.0 V . The peak current is 75 mA . What is the value of the capacitance C in nF?   

B: An FM radio station broadcasts at a frequency of 90 MHz . What inductance, L, should be paired with a 9.0 pF capacitor to build a receiver circuit for this station in microH?

C: A 12 km long, 230 kV aluminum transmission line delivers 40 MW to a city. If we assume a solid cylindrical cable, what minimum diameter is needed if the voltage decrease along this run is to be no more than 1.0 % of the transmission voltage? The resistivity of aluminum is 2.7×108m.

Explanation / Answer

A: f = 11 x 10^3 Hz

Vrms = 9 V

Ipeak = 75 mA

Irms = I_peak / sqrt(2) = 53.03 mA

Z = V / I = (9 Volot) / (53.03 x 10^-3 A )

Z = 169.7 ohm

Z = Xc = 1/ 2 pi f C

169.7 = 1 / (2 x pi x 11 x 10^3 x C)

C = 85.3 x 10^-9 F Or 85.3 nF .........Ans

B: f = 1 / 2 pi sqrt(LC)

2 x pi x 90 x 10^6 = 1 / sqrt(9 x 10^-12 x L)

L = 0.35 x 10^-6 H Or 0.35 microH .........Ans

C: deltaV = 230 x 10^3 x 1 / 100 = 2300 Volt

  
P = V^2 / R

R = 2300^2 / (40 x 10^6) = 0.132 ohm

and R = rho L / A

0.132 = (2.7 x 10^-8) (12 x 10^3) / (pi D^2 / 4)

D = 0.056 m

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