A series RLC circuit is driven by a generator of angular frequency ? and maximum

Question

A series RLC circuit is driven by a generator of angular frequency ? and maximum voltage ?m. The phasor diagram for this circuit is shown below at one instant in time. (Recall the phasor rotates CCW around the origin and the specific value of any quantity at a given instant in time is the projection onto the y-axis.)

1)

At the instant shown, compare the magnitude of the voltage across the inductor, resistor, and capacitor:

A) |VL| > |VR| > |VC|

B) |VL| > |VC| > |VR|

C) |VR| > |VL| > |VC|

D) |VR| > |VC| > |VL|

E) |VC| > |VR| > |VL|

F) |VC| > |VL| > |VR|

2)

At the instant shown, VC is __________ and the magnitude of VC is __________.

A) positive, decreasing

B) positive, increasing

C) negative, decreasing

D) negative, increasing

E) positive, constant

F) negative, constant

3)

Which of the following phasor diagrams shows an instant where VL = 0 and VR is at a maximum value?

(a)

(b)

(c)

(d)

4)

Which of the following phasor diagrams gives the correct location of Vgen?

(a)

(b)

(c)

(d)

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5)

Some time later, the current in the circuit is at a minimum (negative) value. At this instant, the magnitude of Vgen is _________.

A) increasing

B) decreasing

C) constant

Explanation / Answer

1) As the magnitude is the projection along the y-axis, we have

D) |VR| > |VC| > |VL|

2) As the projection of the Vc is along negative x-axis, it is negative and since it is rotating anti clockwise the projrction is moving up so magnitude deceases

C) negative, decreasing

3) VR is maximum when it is along +ve y-axis so

answer (c)

4) Since VL and Vc are opposite in direction their resultant will be Vc - VL in the direction of Vc as Vc is more, now VR is perpendicular to (Vc - VL), so the resultant Vgen will be in between these two phasors so the answer is

(a)

5) Since the current is at minimum negative value, Vgen is also at negative maximum and due to anticlockwise rotation it's magnitude will decreasing after this time

B) decreasing

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