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In the given circuit Rt Calculate (a) Current in each branch. (b) Power generated in each resistance. (c )Total power generated in the circuit. (d)Net current drawn from source. (e)Net impedance of the circuit. |
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Answer» Solution :Impedence of each branch `Z_(1)=sqrt(R_(1)^(2)+X_(L)^(2))=sqrt(4^(2)+3^(2))=5` `Z_(2)=sqrt(6^(2)+8^(2))=10` `Z_(3)=sqrt((10)^(2)+(10-10)^(2))=10` (a) Current in each branch `I_(1)=(V)/(Z_(1))=(100)/(5)=20"amp"` `I_(2)=(100)/(10)=10"Amp"` `I_(3)=(100)/(10)=10"Amp"` (b)Power in each branch. `P_(1)=(I_(1))^(2)R_(1)=(20)^(2)(4)=160"watt"` `P_(2)=(I_(2))^(2)R_(2)=(10)^(2)(6)=600"watt"` `P_(3)=(I_(3))^(2)R_(3)=(10)^(2)(6)=1000"watt"` (c )Net power of the circuit. `P=P_(1)+P_(2)+P=3200"watt"` phase difference between voltage & current in each branch. `tanphi_(1)=(X_(L))/(R_(1))=(3)/(4)Rightarrow phi_(1)=37^(@)``tanphi_(2)=(X_(C))/(R_(2))=(8)/(6)Rightarrow phi_(2)=53^(@)` `tanphi_(3)=0 Rightarrow phi_(3)=0`  (d) Net current DRAWN from source. `sqrt((I_(1)cos 37^(@)+I_(2)cos53^(@)+I_(3))^(2)+(I_(1)sin 37^(@)-I_(2)sin 53^(@))^(2))=sqrt1040` (e )Net impendance of the circuit, `Z=(V)/(I)=(100)/(sqrt1040)` |
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