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A 750 Hz, 20 V (rms) source is connected to a resistance of 100 Ω, an inductance of 0.1803 H and a capacitance of 10 μF 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 surroundings) is close to-
- 365 s
- 418 s
- 245 s
- 348 s
Correct answer: 348 s
Solution
At 750 Hz: XL = wL ~ 850 ohm, XC = 1/(wC) ~ 21 ohm, so Z = sqrt(100^2 + (850-21)^2) ~ 834 ohm. I = 20/Z ~ 0.024 A, power in R = I^2R ~ 0.0574 W. Heat needed = 2 J/C x 10 C = 20 J, so t = 20/0.0574 ~ 348 s.
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