📖 Explanation
Supply voltage V is taken as reference. Current in main winding Im=ZmV ⇒Im=6+j4230∠0∘=31.89∠−33.7∘ Staring capacitor (C) wil be connected in series with the auxilary winding, so modified auxiliary winding impedance.
Zm=8+j6−ωCj=8+j(6−ωC1)=8−j(ωC1−6)
Current in auxiliary winding,
Ia=ZaV=8−j(ωC1−6)230∠0∘=∣Ia∣∠tan−1(8ωC1−6)
Capacitor is provided to make angle between Ia and Im90∘.
So,∠Im+∠Ia∠Iatan−1(8ωC1−6)ωC1ωC=90∘=90∘−33.7∘=56.3∘=56.3∘=18=2πf=2π×50rad/sec=176.84μF