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In the circuit shown find (i) the current I (ii) V1 and V2 (iii) Pf. Draw the phasor diagram.
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Given:

(i) Current:

XL1=2πfL=2π×50×0.05=15.71 ΩXL2=2πfL=2π×50×0.1=31.42 Ω

XC=12πfC=12π×50×50×106=63.66 Ω

ˉZ=10+j15.71+20+j31.42j63.66   =30j16.53=34.25<28.85 Ω

I=VZ=20034.25=5.84 A

(ii) V1 and V2 

Let,     ˉI=5.84<0 A

ˉZ1=10+j15.71=18.62<57.52 Ω

ˉV1=ˉZ1ˉI=(18.62<57.52)(5.84<0)=108.74<57.52 V

ˉZ2=20+j31.42j63.66=20j32.24=37.94 <58.19 Ω

ˉV2=ˉZ2 ˉI=(37.94<58.19)(5.84<0)=221.57<58.19 V

(iii) Power Factor

pf=cosϕ=cos(28.85)=0.875 (leading)

(iv) Vector diagram

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