A circuit is constructed with an AC generator, a resistor, capacitor and inducto

Question

A circuit is constructed with an AC generator, a resistor, capacitor and inductor as shown. The generator voltage varies in time as =Va - Vb = msint, where m = 120 V and = 869 radians/second. The values for the remaining circuit components are: R = 72 , L = 62.9 mH, and C = 12.4F.

1)

What is Z, the impedance of the circuit?

2)

What is Imax, the magnitude of the maximum value of the current in the circuit?

3)

What is , the phase angle between the generator voltage and the current in this circuit. The phase is defined to be positive if the generator voltage the current leads, and negative otherwise.

5)

What is VC = Vd - Va, the voltage across the capacitor, at time t = 0? Note that VC is a signed number.

Explanation / Answer

(1)eqiaton of impedence

Z = sqrt( R^2 + (wL - 1/(wC))^2)= sqrt(72^2 + (869*62.9* 10^-3 - 1/(869*12.4* 10^-6))^2)=81.47 ohm

(2)

Imax = V/Z = 120/81.47=1.47 A

(3)

phase angle = tan^-1( (869*62.9* 10^-3 - 1/(869*12.4* 10^-6)))/72)=-27.91 degree

inductor leads the voltage by 90+27.91 = 117.91 degree

inductor will be zero when it gets to 180
so 180-117.91 =62.09degrees to go

t = angle/w

= 62.09*2*pi/360/869

=0.00124 s

(5)

Vc = Vd - Va= 90-27.91 = 62.09 degree

V = I/wC sin(wt - 67.69 ) = 1.47/(869*12.4 * 10^-6)*sin(-62.69)=-121.21 V

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.