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physics help time limited please help The voltage phasor diagram for a certain s

ID: 1290212 • Letter: P

Question

physics help time limited please help

The voltage phasor diagram for a certain series RLC circuit is shown in the figure below. The resistance of the circuit is 21.8 ?, and the frequency is 60.0 Hz.

The voltage phasor diagram for a certain series RLC circuit is shown in the figure below. The resistance of the circuit is 21.8 ?, and the frequency is 60.0 Hz. (a) Find the maximum voltage ?Vmax. V (b) Find the phase angle phi. degree (c) Find the maximum current. A (d) Find the impedance. ? (e) Find the capacitance. ?F (f) Find the inductance of the circuit. H (g) Find the average power delivered to the circuit. W

Explanation / Answer

a)

Vmax=sqrt[VR2+(VL-VC)2]=sqrt[202+(25-15)2]

Vmax=22.36 Volts

b)

Phase angle

o=tan-1(VL-VC/VR) =tan-1(25-15/20) =26.565o

c)

Since

Cos(o)=R/Z

=>Z=R/Cos(o) =21.8/cos(26.565) =24.37 ohms

Maximum current

Imax=Vmax/Z =22.36/24.37 =0.9174 A

d)

Impedance

Z=24.37 ohms

e)

Xc=VC/Imax=15/0.9174=16.35 ohms

since

XC=1/2pifC

=>C=1/2pi*f*XC=1/2pi*60*16.35

C=1.62*10-4 F or 162.23 uF

f)

Inductive reactance

XL=VL/I max=25/0.9174=27.35/0.9142=29.8 ohms

since

XL=2pifL

=>L=XL/2pif =29.91/2pi*60

L=0.0791 H

g)

Average power

Pav=(1/2)VmaxImaxCos(o) =(1/2)*22.36*0.9174*Cos(26.565)

Pav=9.17 Watts