Draw phasor diagram, consider voltage across capacitor as reference and show whether the pf is leading or lagging.
(b) All values are in ΚΩ. Find overall power factor and power absorbed by the overall circuit .
We calculate the parallel combination of and
Now add the resistor R = 10 Ω in series:
To express Zin =10-10jin polar form:
Magnitude:
Phase angle:
Power factor is lagging
Given,
Input voltage: 25 ( Assume peak)
Input Impedance Zin =
Power Factor, pf = cos(41.84০) =0.75(lagging)
Apparent Power ,
=
Real Power Absorbed, = 50.39MW
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Maximum Power Transfer Theorem :
In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.
Let Impedance of,
Xc near the terminal X is Z1=-j10
10 ohm resistance, Z2=10
3 ohm resistance, Z3=3
XL, Z4 =j14
Xc near to source, Z5=-j10
Now,
Zth=[Z5 || (Z3 +Z4) ] + Z2 +Z1
= [ -j10 || (3+j4)] + 100- j10
= 112 - j36
For t<0, the switch is closed.
Capacitor acts as open to DC.
Voltage across the capacitor,
v(0-)= {(12||4)×V}÷{(12||4)+6} = 8VFor t=0, the switch is opened,Voltage across the Capacitor cannot change instantaneously,So, v(0-)= v(0) = 8VAt t>0, The capacitor is discharging.Rth = (12||4) = 3 ohmC= 1/6 FTime constant, Π = Rth×C = 0.5 So, v(t) = v(0)e-t/Π = 8e-t/0.5 =8e-2t V (Ans.)
The initial energy stored in the Capacitor,
W=(1/2)CVo2
= 0.5×0.167×82
= 5.333J (Ans)
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