You have a 200 ohm resistor, a .400-H inductor, and a 6.00-uF capacitor. Suppose

Question

You have a 200 ohm resistor, a .400-H inductor, and a 6.00-uF capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s.
a)what is the impedance of the circuit?
b)what is the current amplitude
c)what are the voltage amplitudes across the resistor and across the conductor
d)what is the phase angle (phi) of the source voltage with respect to the current? Does the source voltage lag or lead the current?

e)Construct the phasor diagram (I, V_R, V_L, V_total) ***The underscore means read it like V subscript R***

Explanation / Answer

a) The total impedance of the circuit is given by Z = R+Xc+XL

Z = R+1/(jC)+jL = 200+j(250*0.4-1/(250*6*10-6))

= 200-566.67j ohms

|Z|= 600.928 ohms

b) Amplitude of current = I = Amplitude of V/|Z|

= 30/600.928 = 0.0499 amp

c) Voltage amplitude across resistor = I*R = 0.0499*200 = 9.98 V

Voltage amplitude across capacitor = I*|Xc|= 0.0499*666.67=33.267 V

d) Assuming the voltage at zero, phase angle of current relative to voltage is given by,

angle(V/z) = angle(1/(200-566.67j)) = angle(200+566.67j) = 70.560

Therefore voltage lags current by 70.560

e) The current phasor leads the total voltage phasor by 70.560 and rotates with the same angular velocity that is 250 rad/s. Same is the case for V_R and V_C lags the current phasor by 900 and V_L leads it by 900

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