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In the circuit shown find
(i) the current I (ii) V1 and V2 (iii) Pf. Draw the phasor diagram.
1 Answer
written 3.9 years ago by |
Given:
(i) Current:
XL1=2πfL=2π×50×0.05=15.71 ΩXL2=2πfL=2π×50×0.1=31.42 Ω
XC=12πfC=12π×50×50×10−6=63.66 Ω
ˉZ=10+j15.71+20+j31.42−j63.66 =30−j16.53=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+j31.42−j63.66=20−j32.24=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