Example 6.2 : A single phase motor connected to 400 V, 50 Hz supply takes 31.7A at a power factor of 0.7 lagging. Calculate the capacitance required in parallel with the motor to raise the power factor to 0.9 lagging.

400 V, 50 Hz সরবরাহের সাথে সংযুক্ত একটি একক ফেজ মোটর 0.7 ল্যাগিং এর পাওয়ার ফ্যাক্টরে 31.7A নেয়। পাওয়ার ফ্যাক্টরকে 0.9 ল্যাগিং-এ বাড়াতে মোটরের সাথে সমান্তরালে প্রযোজনীয় ক্যাপাসিট্যান্স নির্ণয় করুন।

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.)