SOLUTION: The potential difference across a circuit is given by the complex number V = 40 + j35 volts and the current is given by the complex number I = 6 + j3 amps a) sketch the

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Question 697149: The potential difference across a circuit is given by the complex number
V = 40 + j35 volts
and the current is given by the complex number
I = 6 + j3 amps
a) sketch the appropriate phasors on an Argand diagram.
b) find the phase difference (i.e. the angle Φ )between the phasors for voltage
V and the current I.
c) Find the power (watts) given that P = V x I x cos Φ
Answer by KMST(5328) About Me  (Show Source):
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V = 40 + j35 volts and I = 6 + j3 amps
a) sketch the appropriate phasors on an Argand diagram.


b) find the phase difference
The angle alpha between the voltage V and the real, x-axis can be found from
tan%28alpha%29=35%2F40=0.875 --> alpha+=+0.71883 radians (rounded)
The angle beta between the current I and the real, x-axis can be found from
tan%28beta%29=3%2F6=0.5 --> beta+=+0.46365 radians (rounded)
We can calculate very close approximations of phi and cos%28phi%29
phi=alpha-beta=0.71883-0.46365=0.25518 radians (approx 14.6%5Eo in degrees)
cos%28phi%29=cos%280.25518%29=0.9676 (rounded)

c) Find the power (watts) given that P = V x I x cos Φ
The magnitudes of V and I are
V=sqrt%2840%5E2%2B35%5E2%29=53.151 (rounded)
I=sqrt%286%5E2%2B3%5E2%29=6.7082 (rounded)
P=V%2AI%2Acos%28phi%29=53.151%2A6.7082%2A0.9676=highlight%28345%29watt