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A 750 Hz, 20 V (rms) source is connected...

A 750 Hz, 20 V (rms) source is connected to a resistance of `100 Omega`, an inductance of 0.1803 H and a capacitance of `10 mu F` all in series. The time in which the resistance (heat capacity `2 J//.^@C`) will get heated by `10^@C`. (assume no loss of heat to hte surroundings) is close to :

Text Solution

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`z=sqrt((X_(L)-X_(C))^(2)+R^(2))`
`omega=2npi=2(750)pi=1500 pi`
`X_(L)=omega_(L)=(1500pi)(0.18)=848.5 Omega`
`X_(C)=1/(omegaC)=10^(6)/(1500pi)=212.12 Omega`
`z=sqrt((636.4)^(2)+(100)^(2))`
`=100sqrt((6.364)^(2)+12)`
=`100x6.44~=644 Omega`
`tan phi=(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)=epsilon_(rms)/z=20/644A`
`H=(i_(rms))^(2)RT=(20/644)^(2)(100)t`
`(ms)(Deltatheta)=(20/644)^(2) (100)t`
`(2)(10)=(20/644)^(2) (100)t`
`t=(644/20)^(2)xx1/100xx20`
`t=207.36 sec`
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