Transients
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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
In such cases, as seen from , the current consists of a steady-state component and a transient component. The equation of the resultant current isi = Imsin(ωt - φ)(steady-state current) + Imsinφet/λ (transient current) where Im = Vm/Z; φ = tan-1(XL/R); λ = L/R secondR = 10Ω; XL = 314 x 0.1 = 31.4ΩRead more
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
See lessTransient current in an R-L-C circuit is oscillatory when
(a) R = 0
(b) R > 2√(L/C)
(c) R < 2√(L/X)
(d) R = √(L/C)
Correct option (C) R < 2√(L/C)
Correct option (C) R < 2√(L/C)
See lessA 1.0 H choke has a resistance of 50 Ω . This choke is supplied with an a.c. voltage given by e = 141 sin 314 t. Find the expression for the transient component of the current flowing through the choke after the voltage is suddenly switched on.
The equation of the transient component of the current isit = Imsinφe-t/λHere, λ = L/R = 1/50 = 0.02 second ; Z = 50 + j 314 = 318 ∠ 80.95ºIm = Vm/Z = 141/318 = 0.443 A; sin 80.95º = 0.9875∴ it = 0.443 × 0.9875 e–t/0.02 = 0.4376e–t/0.02
The equation of the transient component of the current is
it = Imsinφe-t/λ
Here, λ = L/R = 1/50 = 0.02 second ; Z = 50 + j 314 = 318 ∠ 80.95º
Im = Vm/Z = 141/318 = 0.443 A; sin 80.95º = 0.9875
∴ it = 0.443 × 0.9875 e–t/0.02 = 0.4376e–t/0.02
See lessThere are no transients in pure resistive circuits because they
(a) offer high resistance
(b) obey Ohm’s law
(c) have no stored energy
(d) are linear circuits.
(c) have no stored energy
(c) have no stored energy
See lessTransient currents in electrical circuit are associated with
(a) inductors
(b) capacitors
(c) resisters
(d) both (a) and (b).
(d) both (a) and (b).
(d) both (a) and (b).
See lessDouble-energy transients are produced in circuits consisting of
(a) two or more resistors
(b) resistance and inductance
(c) resistance and capacitance
(d) resistance, inductance and capacitance.
(d) resistance, inductance and capacitance.
(d) resistance, inductance and capacitance.
See lessThe transients which are produced due to sudden but energetic changes from one steady state of a circuit to another are called ……. transients.
(a) initiation
(b) transition
(c) relaxation
(d) subsidence
(b) transition
(b) transition
See lessA circuit of resistance 10 Ω and inductance 0.1 H in series has a direct voltage of 200 V suddenly applied to it. Find the voltage drop across the inductance at the instant of switching on and at 0.01 second. Find also the flux-linkages at these instants.
(i) Switching instantAt the instant of switching on, i = 0, so that iR = 0 hence all applied voltage must drop across the inductance only. Therefore, voltage drop across inductance = 200 V. Since at this instant i = 0, there are no flux-linkages of the coil. (ii) When t = 0.01 second As time passes,Read more
(i) Switching instant
At the instant of switching on, i = 0, so that iR = 0 hence all applied voltage must drop across the inductance only. Therefore, voltage drop across inductance = 200 V. Since at this instant i = 0, there are no flux-linkages of the coil.
(ii) When t = 0.01 second
As time passes, current grows so that the applied voltage is partly dropped across the resistance and partly across the coil. Let us first find iR drop for which purpose, we need the value of i at t = 0.01 second.
Now, time period of the circuit is λ = L/R = 0.1/10 = 0.01 second. Since the given time happens to be equal to time constant,
∴ i = (200/10) × 0.632 = 12.64 A; iR = 152.64 × 10 = 126.4 V
Drop across inductance = √(2002 – 126.42) = 155V
Now, L = NΦ/i or NΦ = Li
∴ Flux-linkages Li = 0.1 × 12.64 = 1.264 Wb-turns.
See lessTransient disturbance is produced in a circuit whenever
(a) it is suddenly connected or disconnected from the supply
(b) it is shorted
(c) its applied voltage is changed suddenly
(d) all of the above.
(d) all of the above.
(d) all of the above.
See lessThe transient current in a loss-free L-C circuit when excited from an ac source is a/ an ….. sine wave.
(a) over damped
(b) undamped
(c) under damped
(d) critically damped.
(b) undamped
(b) undamped
See less