Transient Response · Network Theory · GATE ECE

Marks 1

In the circuit given below, the switch $S$ was kept open for a sufficiently long time and is closed at time $t = 0$. The time constant (in seconds) of the circuit for $t > 0$ is _______ .

GATE ECE 2024

In the circuit shown below, switch S was closed for a long time. If the switch is opened at t = 0, the maximum magnitude of the voltage $$\mathrm{V_R}$$, in volts, is __________ (rounded off to the nearest integer).

GATE ECE 2023

The switch has been in position 1for a long time and abruptly changes to position 2 at t = 0.

If time t is in seconds, the capacitor voltage V_C (in volts) for t>0 is given by

GATE ECE 2016 Set 2

In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The energy (in $$\mu J$$) taken from the 3V source to charge the 0.1$$\mu$$F capacitor from 0V to 3V is

GATE ECE 2015 Set 1

A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage V_S, the resistance R, the capacitance C, and the current i(t) is given below: $$$V_{s\;}=\;Ri(t)+\frac1c\int_0^ti(u)du$$$ Which one of the following represents the current f(t)?

GATE ECE 2014 Set 3

In the figure shown, the ideal switch has been open for a long time. If it is closed at t=0, then the magnitude of the current (in mA) through the $$4k\Omega$$ resistor at t = 0⁺ is _______.

GATE ECE 2014 Set 2

In the following figure, C₁ and C₂ are ideal capacitors. C₁ has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is.

GATE ECE 2012

If the unit step response of a network is $$(1-e^{-\alpha t})$$, then its unit impulse response is

GATE ECE 2011

In the following circuit, the switch S is closed at t=0. The rate of change of current $$\frac{di}{dt}(0^+)$$ is given by

GATE ECE 2008

The condition on R, L and C such that the step response y(t) in figure has no oscillations, is

GATE ECE 2005

For the R-L circuit shown in Fig, the input voltage. v_i(t) = u (t) The current i(t) is

GATE ECE 2004

In figure, the switch was closed for a long time before opening at t = 0. the voltage V_x at t = 0⁺ is

GATE ECE 2002

A ramp voltage, v(t) = 100 t Volts, is applied to an RC differentiating circuit with R = $$5k\Omega$$ and C = $$4\mu F$$.The maximum output voltage is

GATE ECE 1994

Marks 2

The switch S$$_1$$ was closed and S$$_2$$ was open for a long time. At t = 0, switch S$$_1$$ is opened and S$$_2$$ is closed, simultaneously. The value of i$$_\mathrm{c}$$(0$$^+$$), in amperes, is

GATE ECE 2023

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is _______.

GATE ECE 2018

The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0. The current i(t) (in ampere) at t = 0.5 seconds is ________

GATE ECE 2017 Set 2

The switch S in the circuit shown has been closed for a long time. It is opened at time t = 0 and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop.

The steady state magnitude of the capacitor voltage V_C (in volts) is ____________.

GATE ECE 2016 Set 2

Assume that the circuit in the figure has reached the steady state before time t = 0 when the 3 Ω resistor suddenly burns out, resulting in an open circuit. The current i(t) (in ampere) at t = 0⁺ is ____________.

GATE ECE 2016 Set 3

In the circuit shown, the initial voltages across the capacitors C₁ and C₂ are 1 V and 3 V, respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in the resistor R until steady state is reached is _______________.

GATE ECE 2015 Set 2

In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of v_c(t) (in Volts) at t= 1 sec is ___________.

GATE ECE 2015 Set 1

In the circuit shown in the figure, the value of V₀(t) (in Volts) for $$t\rightarrow\infty$$ is ______.

GATE ECE 2014 Set 4

In the figure shown, the capacitor is initially uncharged. Which one of the following expressions describes the current I(t) (in mA) for t > 0?

GATE ECE 2014 Set 2

In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t=0. The current i(t) at a time t after the switch is closed is

GATE ECE 2011

In the circuit shown, the switch S is open for a long time and is closed at t=0. The current i(t) for t ≥ 0⁺ is

GATE ECE 2010

The switch in the circuit shown was on position ‘a’ for a long time and is moved to position ‘b’ at time t = 0. The current i(t) for t > 0 is given by

GATE ECE 2009

The time domain behavior of an RL circuit is represented by $$$\mathrm L\frac{\mathrm{di}\left(\mathrm t\right)}{\mathrm{dt}}+\mathrm{Ri}\;=\;{\mathrm V}_0\left(1\;+\;\mathrm{Be}^{-\mathrm{Rt}/\mathrm L}\;\sin\;\mathrm t\right)\mathrm u\left(\mathrm t\right)$$$ For an initial current of i(0) = $$\frac{{\mathrm V}_0}{\mathrm R}$$, the steady state value of the current is given by

GATE ECE 2009

The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t).

For t > 0, the output voltage V_c(t) is

GATE ECE 2008

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage V_c(t) across the capacitor is given by

GATE ECE 2008

The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t).

For t > 0, the voltage across the resistor is

GATE ECE 2008

In the circuit shown, V_C is 0 volts at t = 0 sec. For t > 0, the capacitor current i_C(t), where t is in seconds, is given by

GATE ECE 2007

A 2mH inductor with some initial current can be represented as shown below, where s is the Laplace Transform variable. The value of initial current is:

GATE ECE 2006

In the figure shown below, assume that all the capacitors are initially uncharged. If ν_i(t) = 10 u(t) Volts, ν₀(t) is given by

GATE ECE 2006

A square pulse of 3 volts amplitude is applied to C-R circuit shown in figure. The capacitor is initially uncharged. The output voltage v₀ at time t=2 sec is

GATE ECE 2005

The circuit shown in Fig, has initial current $${\mathrm i}_\mathrm L\left(0^-\right)\;=\;1\;\mathrm A$$ through the inductor and an initial voltage $${\mathrm v}_\mathrm C\left(0^-\right)\;=\;-1\;\mathrm V$$ across the capacitor. For input v(t) = u(t), the Laplace transform of the current i(t) for t ≥ 0 is

GATE ECE 2004

The circuit is given in figure.Assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

At t = 0⁺, the current i₁ is

GATE ECE 2003

The circuit is given in figure.Assume that the switch S is in position 1 for a long time and thrown to position 2 at t = 0.

I₁(s) and I₂(s) are the Laplace transforms of i₁(t) and i₂(t) respectively. The equations for the loop currents I₁(s) and I₂(s) for the circuit shown in figure, after the switch is brought from position 1 to position 2 at t = 0, are

GATE ECE 2003

The voltage V_C1, V_C2 and V_C3 across the capacitors in the circuit in Fig., under steady state, are respectively

GATE ECE 1996

For the compensated attenuator of figure, the impulse response under the condition $$R_1C_1\;=\;R_2C_2$$ is:

GATE ECE 1992

If the Laplace transform of the voltage across a capacitor of value of $$\frac12\;\mathrm F$$ is $$V_C\;\left(s\right)\;=\;\frac{s\;+\;1}{s^3\;+\;s^2\;+\;s\;+\;1}$$ , the value of the current through the capacitor at t = 0⁺ is

GATE ECE 1990

A 10 Ω resistor, a 1 H inductor and 1 $$\mathrm{μF}$$ capacitor are connected in parallel.The combination is driven by a unit step current.Under the steady state condition, the source current flows through

GATE ECE 1989

Marks 3

In the circuit shown in Fig (a) - (c), assuming initial voltages across capacitors and current through the inductors to be zero at the time of switching (t=0), then at any time t>0.

Match each of the items of Set 1, with the appropriate item of the Set 2.

GATE ECE 1996 Network Theory - Transient Response Question 14 English

Set 2

(1) current increases monotonically with time
(2) current decreases monotonically with time
(3) current remains constant at V/R
(4) current first increases, then decreases
(5) no current can ever flow

GATE ECE 1996

Marks 5

The switch in Fig. has been in position $$1$$ for a long time and is then moved to position $$2$$ at $$t\, = \,0$$.

(a) Determine $${V_C}\left( {{0^ + }} \right)$$ and $${I_{_L}}\left( {{0^ + }} \right)$$
(b) Determine $${{d{V_C}\left( t \right)} \over {dt}}\,\,$$ at $$t\, = \,{0^ + }$$
(c) Determine $${{V_C}\left( t \right)}$$ for $$t > 0$$

GATE ECE 2002

The circuit shown in Fig. is operating in steady-state with switch $${S_1}$$ closed. The switch $${S_1}$$ is opened at $$t\, = \,0$$.

(a) Find $${i_L}\left( {{0^ + }} \right)$$.
(b) Find $${e_1}\left( {{0^ + }} \right)$$.
(c) Using nodal equations and Laplace transform approach, find an expression for the voltage across the capacitor for all $$t\, = \,0$$.

GATE ECE 2001

The network $$N$$ in Fig. consists only of two elements: a resistor of $$1\Omega $$ and an inductor of L Henry. $$A$$ $$5$$ $$V$$ source is connected at the input at $$t\, = \,0$$ seconds. The inductor current is zero at $$t\, = \,0$$. The output voltage is found to be $$5{e^{ - 3t}}\,\,V,$$ for $$t\, = \,0$$.

(a) Find the voltage transfer function of the network.
(b) Find L, and draw the configuration of the network.
(c) Find the impulse response of the network.

GATE ECE 2000

In the circuit of figure, the switch $$'S'$$ has remained open for a long time. The switch closes instantaneously at $$ t = 0$$.

(a) Find $${V_0}$$ for $$t \le 0$$ and as $$t \to \infty $$.
(b) Write an expression for $${V_0}$$ as a function of time for $$0 \le t \le \infty $$.
(c) Evaluate $${V_0}$$ at $$t = 25\,\,\mu $$sec.

GATE ECE 1999

The circuit shown in the figure, is initially in its steady state. Switch is opened at t = 0.
(1) Determine the initial voltage, V_C(0^-), across the capacitor, and the initial current, i_L(0^-) , through the indicator.
(2) Calculate the voltage, V_L(t) , across the inductance for t > 0.

GATE ECE 1994

In the following circuit the capacitance varies as C = KQ, where K is a constant equal to 0.5 Farads/Coulomb and Q, the charge on the capacitor in Coulombs. Determine the current through the circuit and sketch the voltage waveform across the capacitor (V_C) for a step input V_i as shown in figure.

GATE ECE 1993

The network shown in figure is initially under steady-state condition with the switch in position 1. The switch is moved from position 1 to position 2 at t = 0. Calculate the current i(t) through R₁ after switching.

GATE ECE 1991

Marks 8

The circuit shown below is initially in a steady state condition. At $$t = 0$$, the switch '$$S$$' is opened.

(i) Determine the initial voltage $${V_c}\left( {{0^ - }} \right)$$ across the capacitor and initial current $${i_L}\left( {{0^ - }} \right)$$ through the inductor.
(ii) Find the voltage $${v_L}\left( t \right)$$ across the inductor for $$t > 0$$.

GATE ECE 1988

Marks 10

The switch $$S$$ in figure is thrown to position $$'a'$$ at $$t = 0$$. At $$t = 1$$ second, the switch is thrown to position $$'b'$$. Find the current through $${R_2}$$ for $$ t > 1$$ sec.

GATE ECE 1990