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 μ 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 the surroundings) is close to :

Step-by-step solution

The AC circuit is shown below. Here, R = 100 ,   X L = L ω = 0 . 1803 × 750 × 2 π = 850 Ω The capacitive reactance X c = 1 Cω = 1 10 - 5 × 2 π × 750 = 21 . 23   Ω Total impedance Z = R 2 + X L - X C 2 = 100 2 + 850 - 21 . 23 2 = 834 . 77 ≈ 835 The heat loss H = i rms 2 Rt = ms ∆ t 20 835 × 20 835 × 100 t = 2 × 10 t = 348 . 61   sec