please show all the work to get 5/5 For the circuit shown in Fig. 3: a- Use noda

Question

please show all the work to get  5/5

For the circuit shown in Fig. 3:
a- Use nodal analysis to find the voltage 1 V assuming? is 100 rad / sec.
b- Find the amount of active power in watts delivered to each element and state whether it is
generated (G) or absorbed (A).
c- Find the amount of reactive power in VARs delivered to each element and state whether it is
generated (G) or absorbed (A).

For the circuit shown in Fig. 3: Use nodal analysis to find the voltage 1 V assuming? is 100 rad / sec. Find the amount of active power in watts delivered to each element and state whether it is generated (G) or absorbed (A). Find the amount of reactive power in VARs delivered to each element and state whether it is generated (G) or absorbed (A).

Explanation / Answer

w=100 rad/sec

so capacitance=1/(j*500*10^(-6)*100)=-20j ohms

using nodal analysis:

at the junction of 10 ohm and 500 uF,

40<0 = (V1/10) + (V1-(-3*V1/2))/(15-20j)

V1=200-j100 volts

(ans.)

b.current through 10 ohm=V1/10=20-j10 A

so active power =20^2*10=4000 W,absorbed

current through 500 uF and 15 ohm=2.5*V1/(15-20j)

=20+10j

so active power absorbed by capacitor=0

active power absorbed by 15 ohm=20^2*15=6000 W

c.reactive power absorbed by 500uF=10^2*20=2000 VAR

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