Question

voitago Δν.ao sn 100e, where Δν is in vons and ris in seconds is applied to a series RLCaout with L-145 miH, C.99.0μF.and R. 71.0Ω (a) What is the impedance of the circuit? 8.60-3 What is the angular frequency of th source? (c) Determine the numerical value for ω inthe equatori-hax sin (ar- radis (d) Determine the numerical value for φί' the equatori.hax sin(ar-ต rad

Answer 1

Given that,

$\Delta$ V = 43 sin (100t)

so, w = 100 rad/s

(a)

capacitive reactance, xC = 1 / wC

xC = 1 / 100*99*10^(-6) = 101.01

lnductive reactance, xL = wL

xL = 100*0.145 = 14.5

lmpedence of the circuit, Z = sqrt (R^2 + (xL - xC)^2)

Z = sqrt [71^2 + (14.5 - 101.01)^2]

Z = 111.91 ohm

(b)

maximum current, lmax = V / Z

lmax = 43 / 111.91

lmax = 0.384 A

(c)

w = 100 rad/s

(d)

tan $\phi$ = (xL - xC) / R

$\phi$ = tan^-1 [(14.5 - 101.01) / 71]

$\phi$ = -50.6 deg