In the circuit, the voltage source frequency, amplitude and phase are 16 MHz, 42

Question

In the circuit, the voltage source frequency, amplitude and phase are 16 MHz, 42 V and 1.5 rad correspondingly;
R1=7 kOhm, L1= 55 uH (u=micro), C1= 2.6 pF, R2=2 kOhm.
Find the average and reactive powers delivered by the voltage source into the circuit (ignore the signs).

In the circuit, the voltage source frequency, amplitude and phase are 16 MHz, 42 V and 1.5 rad correspondingly; R1=7 kOhm, L1= 55 uH (u=micro), C1= 2.6 pF, R2=2 kOhm. Find the average and reactive powers delivered by the voltage source into the circuit (ignore the signs).

Explanation / Answer

Given data is f=16MHz

V=42/_1.5 rad

R1=7k ohms

R2=2k ohms

L1=55uH

C1=2.6pF

XL1=2x?x16x10^6X58x10^-6=j5.5k ohms

XC1=[1/2x?x32x10^6X2.8x10^-12]=-j3.825k ohms

Now from the circuit R2 in series with -jXC1=(2-j3.825)k ohms ---(1) in parallel with jXL1

i.e (10.48-j4.26)k ohms ----(2) this is in series with 7k ohms resistance R1

Req=(17.406-j4.3) k ohms

Now total power S= V^2/Req= (42/_1.5)^2/[(17.406-j4.3)x10^3]

S=(-97.88-j9.8) kW =P+jQ

Active Power =P=97.88 kW

Average power=P/2=48.94kW

Reactive Power Q=9.8 kW

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