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A 50-Hz sinusoidal voltage of maximum value of 400 V is applied to a series circuit of resistance 10 Ω and inductance 0.1 H. Find tan expression for the value of the current at any instant after the voltage is applied, assuming that voltage is zero at the instant of application. Calculate its value 0.02 second after switching on
A 50-Hz sinusoidal voltage of maximum value of 400 V is applied to a series circuit of resistance 10 Ω and inductance 0.1 H. Find tan expression for the value of the current at any instant after the voltage is applied, assuming that voltage is zero at the instant of application. Calculate its value 0.02 second after switching on
In such cases, as seen from , the current consists of a steady-state component and a transient component. The equation of the resultant current is
i = Imsin(ωt – φ)(steady-state current) + Imsinφet/λ (transient current)
where Im = Vm/Z; φ = tan-1(XL/R); λ = L/R second
R = 10Ω; XL = 314 x 0.1 = 31.4Ω; Z = 10 + j31.4 = 33∠72
3º
Im = 400/33 = 12.1A; φ = 72.3º = 1.26 rad.
sinφ = sin72.3º = 0.9527; λ = 0.1/10 = 1/100 second
i = 121{sin(314t – 1.262) + 0.9527e100t}
Substituting t = 0.02 second, we get
i = 12.1 (sin (314 × 0.02 – 1.262) + 0.9527 e–2}
= 12.1 (sin 5.02 + 0.9527 e–2) = 12.1 (sin 288º + 0.9527 e–2)
= 12.1 (– sin 72º + 0.9527 × 0.1353)
= 12.1 (– 0.9511 + 0.1289) = –9.95 A