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A 750 Hz, 20 V source is connected to as...

A `750 Hz, 20 V` source is connected to as resistance of `100 Omega` an inductance of `0.1803 H` and a capacitance of `10 muF` all in sereis.Calculate the time in which the resistance (thermalcapacity `2J//.^(@)C`) wil get heated by `10^(@)C`.

Text Solution

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`z=sqrt((X_(L)-X_(C))^(2)+R^(2))`
`omega=2nnpi=2(750)pi=1500pi`
`X_(L)=omega_(L)=(1500pi)(0.18)=848.5Omega`
`X_(C)=(1)/(omegaC)=(10^(6))/(1500pi)=212.12Omega`
`=100xx6.44cong644Omega`
`tanphi=(X_(L)-X_(C))/(R)=(848.5-212.12)/(100)=6.36`
`(c) cos phi=(R)/(z)=(100)/(644)=0.155`
(b) impedence is constant as n is constant
`(d) i_("rms")=(epsi_("rms"))/(z)=(20)/(644)A`
`H=(i_("rms"))Rt=((20)/(644))^(2)(100)t Rightarrow (rms)(Deltatheta)=((20)/(644))^(2)(100t)`
`(2)(10)=((20)/(644))^(2)(100)t Rightarrow t=((644)/(20))^(2)xx(1)/(100)xx20Rightarrow t=207.36sec`
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