Question

a generator supplying alternating voltage is connected in series with a resistor, a capacitor and an inductor. the generator we use in the physics lab is called function generator. let's have the function generator with a maximum voltage of 140, with omega= 3.8 x 10^5 rad/s. let R=1000 ohms, C=56 nF , L=2.5 mH. a)what is thecapacitive reactance? b) what is the inductive reactance? c) what is the impidance of the circuit? d) determine the current amplitude. e) determine the phase angle between the source voltage and the current. f) construct the phasor diagram and display correctly all the voltage phasirs?

Answer 1

given
V_max = 140 V
w = 3.8*10^5 rad/s
R = 1000 ohms
C = 56 nF = 56*10^-9 F
L = 2.5 mH = 2.5*10^-3 H

a) capacitive reactance, Xc = 1/(w*C)

= 1/(3.8*10^5*56*10^-9)

= 47 ohms <<<<<<<<<<---------------Answer

b)) inductive reactance, XL = w*L

= 3.8*10^5*2.5*10^-3

= 950 ohms <<<<<<---------------Answer

c) impidance of the circuit,
z = sqrt(R^2 + (XL - Xc)^2)

= sqrt(1000^2 + (950 - 47)^2)

= 1347 ohms <<<<<<<----------Answer

d) current amplitude, I_max = V_max/z

= 140/1347

= 0.104 A

e) phase angle, phi = tan^-1( (XL - Xc)/R)

= tan^-1( (950 - 47)/1000)

= 42.1 degrees

here current lags source voltage by 42.1 degrees

f)