Question

For values of L = 1H; C=1nF; R = 5kΩ, what is the resonant frequency of the

circuit? What is the natural frequency of the circuit? What is the Q value? If the coil is

wound from 42 gauge copper wire, what is the length of wire used in the coil?

Fig Q1

Answer 1

Pupedance (7) = (R+52) // %ec Z - (R+SL)• Yọc 1. Risit the RIBL (Z) = - PRETS2LCHI = (Rj6L) CR-W2C) - jWRC) (1-w2Rc)2+(WRC)”. =) Z(jw) - R+WL -W2LC +1+3WRC = R(1-w2cc) + : [WL (1-6046) -WRC] 11-W2LC)2+ (WRC)? frequency means sterm =0. =) Resonant So, wl (1-2LC)-RC (i-whe)? WRC)2 = 0 -) w [l (twPLC) –RC] = 0. 1[1-w?LC)-RC =0 =) L-W2L2C-RC=0. =) W222C=L-rc. 120 =) W2= |- RC resonant frequency (w) = fue = 5 ✓ 1x109 = 316221698 rad/sec =) here second onder equaaton is nect SRC+1=0 =) SR LC4 BRCA1 = 82 + 8 + te=0 - 8²42&unstan"=0 rad/80 natusal forequency ana te stripe = Jiot = 31622.7766 Itum = { =) 24 = Bauw = 0.158114 Q = 6.325

h 42 guage copper turns =) N = 1000 Diameter =) 0.0633 mm. 14D10 &12 =2f ( W = 31692.7766) / RT L = 1480.0639 X 1000 x 10?m 217618104 meters. 131622.7766 l 21