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`.

Options

A. 245s
B. 365 s
C. 418 s
D. 348 s

Answer

D

Explanation

`f=750 Hz,V_(rms ) = 20 ,V R = 100 omega , L = 0.1803 H`
` S= 2J //^@ C`
` Z= sqrt(R^2 + (X_L -X_C )^2)=sqrt(R^2 +( 2 pi f L -(1)/( 2 pi f c ))^2)`
` |Z|= sqrt((100)^2+(2xx3.14xx750xx0.1803- (1)/( 2xx3.14xx750xx10^(-5)))`
`|Z|= 834 Omega `
In AC
` P=V_(rms) I_(rms) cos phi`
` P=(V_(rms) .(V_(rms))/(|Z|).(R )/(|Z|))`
` P=((V_(rms))/( |Z|))^2 R`
` P= ((20)/(834 ))^2 xx 100 = 0.0575J //S`
`p xx t = S Delta theta`
` t= ( 2(10))/( 0.0575)`
`t= 348 ` sec