11 + Interview Questions in GENERAL QA IN TRANSIENTS Page 1 InterviewSolution

1.	A 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.
Answer» (i) Switching instant At the instant of switching on, i = 0, so that i_R = 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.

1.

A 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.

Answer»

(i) Switching instant

At the instant of switching on, i = 0, so that i_R = 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.

Discussion

2.	A 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.
Answer» The equation of the transient component of the current is i_t = I_msinφe^-t/λ Here, λ = L/R = 1/50 = 0.02 second ; Z = 50 + j 314 = 318 ∠ 80.95º I_m = V_m/Z = 141/318 = 0.443 A; sin 80.95º = 0.9875 ∴ i_t = 0.443 × 0.9875 e^–t/0.02 = 0.4376e^–t/0.02

2.

A 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.

Answer»

The equation of the transient component of the current is

i_t = I_msinφe^-t/λ

Here, λ = L/R = 1/50 = 0.02 second ; Z = 50 + j 314 = 318 ∠ 80.95º

I_m = V_m/Z = 141/318 = 0.443 A; sin 80.95º = 0.9875

∴ i_t = 0.443 × 0.9875 e^–t/0.02 = 0.4376e^–t/0.02

Discussion

3.	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
Answer» 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 = I_msin(ωt - φ)(steady-state current) + I_msinφe^t/λ (transient current) where I_m = V_m/Z; φ = tan^-1(X_L/R); λ = L/R second R = 10Ω; X_L = 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

3.

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

Answer»

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 = I_msin(ωt - φ)(steady-state current) + I_msinφe^t/λ (transient current)

where I_m = V_m/Z; φ = tan^-1(X_L/R); λ = L/R second

R = 10Ω; X_L = 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

Discussion

4.	In an R-L circuit connected to an alternating sinusoidal voltage, size of transient current primarily depends on (a) the instant in the voltage cycle at which circuit is closed (b) the peak value of steady-state current (c) the circuit impedance (d) the voltage frequency.
Answer» (a) the instant in the voltage cycle at which circuit is closed

Discussion

5.	Double-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.
Answer» (d) resistance, inductance and capacitance.

Discussion

6.	The 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
Answer» (b) transition

Discussion

7.	Transient currents in electrical circuit are associated with(a) inductors (b) capacitors (c) resisters (d) both (a) and (b).
Answer» (d) both (a) and (b).

Discussion

8.	Transient 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)
Answer» Correct option (C) R < 2√(L/C)

Discussion

9.	The 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.
Answer» (b) undamped

Discussion

10.	There 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.
Answer» (c) have no stored energy

Discussion

11.	Transient 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.
Answer» (d) all of the above.

Discussion

Explore topic-wise InterviewSolutions in .

A 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.

A 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.

In an R-L circuit connected to an alternating sinusoidal voltage, size of transient current primarily depends on (a) the instant in the voltage cycle at which circuit is closed (b) the peak value of steady-state current (c) the circuit impedance (d) the voltage frequency.

Double-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.

The 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

Transient currents in electrical circuit are associated with(a) inductors (b) capacitors (c) resisters (d) both (a) and (b).

Transient current in an R-L-C circuit is oscillatory when (a) R = 0 (b) R &gt; 2√(L/C)(c) R &lt; 2√(L/X)(d) R = √(L/C)

The 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.

There 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.

Transient 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.

Transient 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)