1 The FM radio band covers the frequency range 88108 MHz Par

1. The FM radio band covers the frequency range 88-108 MHz.
Part A
If the variable capacitor in an FM receiver ranges from 14.9 pF to 22.4 pF , what inductor should be used to make an LC circuit whose resonant frequency spans the FM band?
L= H

2. A 470 resistor, 10Fcapacitor, and 750-mH inductor are each connected across 6.3-Vrms, 60-Hz AC power sources.
Part A
Find the rms current in resistor.
Express your answer using two significant figures.
I=A
Part B
Find the rms current in capacitor.
Express your answer using two significant figures.
I= A
Part C
Find the rms current in inductor .
Express your answer using two significant figures.

I=A

Solution

At resonance, reactance of C = reactance of L

2 pi f L = 1 / 2 pi f C

L = 1 / 4 pi² f² C = 1 / ( 4 pi² (108 * 10⁶)² (14.9 * 10^-12) )

= 1.46 * 10^-7 H

The other end

L = 1 / 4 pi² f² C = 1 / ( 4 pi² (88 * 10⁶)² (22.4 * 10^-12) )

= 1.46 * 10^-7 H

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Part A

I_R = V / R = 6.3 / 470 = 0.0134 A

Part B

w = 2 pi * 60 = 376.99 rad/s , X_C= 1 / w C = 265.26

I_C = V / X_C = 0.0238 A

part C

X_L = w L = 376.99 * 750 * 10^-3 = 282.74 ohms

I_L = V / X_L = 0.0223 A