A circuit takes a current of `3 A` at a power factor of 0.6 lagging when connected. to a `115 V- 50 Hz` supply. Another circuit takes a current of `5 A` at a power factor of `0.707` leading when connected to the same supply. If the two circuits are connected in series across a `230 V 50 Hz` supply, then calculate
(a) the current
(b) the power consumed and (c) the power factor

Answer

A, B, C

Explanation

`Z_1=115/3=38.33Omega`
`cosphi_1=R_1/Z_1`
`impliesR_1=Z_1cosphi`
`=(38.33)(0.6)=23Omega`
`X_L=sqrt(Z_1^2-R_1^2)=30.67Omega`
`Z_2=115/2=23Omega`
`R_2=Z_2cosphi_2=(23)(0.707)`
`=16.26`
`X_C=sqrt(Z_2^2-R_2^2)`
`=sqrt((23)^2-(16.26)^2)`
When connected in series,
`R=R_1+R_2=39.26Omega`
`X_L-X_C=14.41Omega`
`:. Z=sqrt(X^2+(X_L-X_C)^2)`
`=41.82 Omega`
(a) `i=V/Z=230/41.82=5.5A`
(b) `P=i^2R=(5.5)62(39.26)`
`=1187.6W~~1.188kW`
(c) Power factor `=cosphi=R/Z =39.26/41.92=0.939`
Since `X_LgtX_C` this power factor is lagging.