একটি সমবায় সার্কিটের প্রয়োগকৃত ভোল্টেজ V(t)=282.8 sin 500t V এবং প্রবাহিত কারেন্ট = i(t) = 5.656 cos(500t -126.87)A যদি সমবায় বর্তনীর একটির প্যারামিটার C=100µF হয় তবে অন্যান্য প্যারামিটার নির্ণয় কর? (The applied voltage of a parallel circuit is V(t) = 282.8 sin 500t V and the current flowing through it is i(t) = 5.656cos(500t - 126.87) A If one of the parameters of the parallel circuit is C = 100µF then determine the other parameters?)

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.

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.R_th = (12||4) = 3 ohmC= 1/6 FTime constant, Π = R_th×C = 0.5 So, v(t) = v(0)e^-t/Π  = 8e^-t/0.5 =8e^-2t V (Ans.)