A 750, Hz,20, V (rms) source is connected to | vedclass

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(C) Given: $f = 750\, Hz$,$V_{rms} = 20\, V$,$R = 100\, \Omega$,$L = 0.1803\, H$,$C = 10\, \mu F = 10 	imes 10^{-6}\, F$,$S = 2\, J/^{\circ}C$,$\Delt

Vedclass · Accepted Answer

$348$

Vedclass · Answer

(C) Given: $f = 750\, Hz$,$V_{rms} = 20\, V$,$R = 100\, \Omega$,$L = 0.1803\, H$,$C = 10\, \mu F = 10 	imes 10^{-6}\, F$,$S = 2\, J/^{\circ}C$,$\Delta T = 10^{\circ}C$.First,calculate the inductive reactance $X_L$ and capacitive reactance $X_C$:$X_L = 2\pi fL = 2 	imes 3.14159 	imes 750 	imes 0.1803 \approx 849.6\, \Omega$.$X_C = \frac{1}{2\pi fC} = \frac{1}{2 	imes 3.14159 	imes 750 	imes 10 	imes 10^{-6}} \approx 21.2\, \Omega$.Calculate the impedance $Z$:$Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{100^2 + (849.6 - 21.2)^2} = \sqrt{10000 + (828.4)^2} \approx \sqrt{10000 + 686246} \approx \sqrt{696246} \approx 834.4\, \Omega$.The power dissipated in the resistor is $P = I_{rms}^2 R = \left(\frac{V_{rms}}{Z}ight)^2 R = \left(\frac{20}{834.4}ight)^2 	imes 100 \approx (0.02397)^2 	imes 100 \approx 0.05746\, W$ (or $J/s$).The heat required is $Q = S \cdot \Delta T = 2\, J/^{\circ}C 	imes 10^{\circ}C = 20\, J$.The time $t$ required is $t = \frac{Q}{P} = \frac{20}{0.05746} \approx 348.07\, s$.Thus,the time is close to $348\, s$.

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