An AC source is connected to an inductance of 100 mH , a capacitance of 100 μ F and a resistance of 120 Ω as shown in figure. The time in which the resistance having a thermal capacity 2 J C - 1 ∘ will get heated by 16 ° C is _____ s .

Step-by-step solution

From the diagram given, Angular frequency ω = 100   rad   s - 1 and V r m s = V 0 2 = 20 2 2 = 20   V . Now, X L = ω L = 100 × 100 × 10 - 3 = 10   Ω and X C = 1 ω C = 1 100 × 100 × 10 - 6 = 100   Ω X L - X C = 10 - 100 = 90   Ω The impedance of the circuit, Z = X L - X C 2 + R 2 = 90 2 + 120 2 = 150   Ω The current in the circuit, i mrs = V rms Z = 20 150   A Power factor cos ϕ = R Z Now V r m s i r m s cos ϕ &#