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A series RLC circuit is connected across a 200 V, 60 Hz supply. It contains a capacitor of capacitive reactance 30 ohm, a non-inductive resistor of 44 ohm, and a coil with inductive reactance 90 ohm and resistance 36 ohm. Find the power dissipated in the coil.

1. 320 W
2. 176 W
3. 144 W
4. 0 W

Correct answer: 144 W

Solution

Total resistance R_total = 44 + 36 = 80 ohm. Net reactance X = XL - XC = 90 - 30 = 60 ohm (inductive). Total impedance Z = sqrt(R_total² + X²) = sqrt(80² + 60²) = sqrt(6400+3600) = sqrt(10000) = 100 ohm. Current I = V/Z = 200/100 = 2 A (rms). Power dissipated in coil = I² * R_coil = 2² * 36 = 4 * 36 = 144 W.

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