A 750 Hz , 20 V ( r m s ) source is connected to a resistance of 100Ω , 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 )

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A 750 Hz , 20 V ( r m s ) source is connected to a resistance of 100Ω , 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 1 0 ∘ C . (assume no loss of heat to the surroundings) is close to :

TestHub · Accepted Answer

The AC circuit is shown below. Here, R = 100 , X L ​ = L ω = 0.1803 × 750 × 2 π = 850Ω The capacitive reactance X c ​ = C ω 1 ​ = 1 0 − 5 × 2 π × 750 1 ​ = 21.23Ω Total impedance Z = R 2 + ( X L ​ − X C ​ ) 2 ​ = 10 0 2 + ( 850 − 21.23 ) 2 ​ = 834.77 ≈ 835 The heat loss H = i r m s 2 ​ Rt = ( m s ) Δ t 835 20 ​ × 835 20 ​ × 100 t = ( 2 ) × 10 t = 348.61 sec

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