R এর মান কত হলে ডিসি কন্ডিশানে ক্যাপাসিটরে সঞ্চিত শক্তি, ইন্ডাক্টরে সঞ্চিত শক্তির সমান হবে?
Calculate R that will make energy stored in the capacitor the same as in the inductor .
Under de condition the capacitor is opened and inductor is shorted. So,
Energy Stored in Capacitor,
Energy Stored in Inductor,
As, energy stored in the capacitor the same as energy stored in the inductor, WC=WL
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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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