An appliance takes a current of 45A at 0.2 power factorlagging. Determine the current to be taken by a bank ofcapacitors in order to improve the power factor to 0.6lagging. Calculate the value of the capacitors inmicrofarads if they are supplied at (a) 240V, (b) 415V, andthe supply frequency is 50Hz.
The easiest way to do this is using complex power S V*I 240*45 10800VA arcos(0.2) 78.5° Q 10800*sin78.5 10,582VARS (volt amperes reactive) P S*cos78.5 2,160W When pf 0.6 S 2,160/0.6 3,600VA Q √3600?-2160?) 2,880VARS 10582-2880 7,702VARS Qc which must be supplied by the capacitors. Qc V?/(1/ωC) C Qc/V?ω 425.6μF at 240V When V 415V S V*I 415*45 18,675VA arcos(0.2) 78.5° Q 18,675*sin78.5 18,298VARS P S*cos78.5 3,735W When pf 0.6 S 3,735/0.6 6,225VA Q √6225?-3735?) 4,980VARS 18,298-4,980 13,318VARS Qc which must be supplied by the capacitors. Qc V?/(1/ωC) C Qc/V?ω 246.1μF at 415V
