Transient Response · Electric Circuits · GATE EE
Marks 1
1
The circuit shown in the figure with the switch S open, is in steady state. After the switch S is closed, the time constant of the circuit in seconds is
GATE EE 2024
2
In the circuit shown below, the switch S is closed at t = 0. The magnitude of the steady state voltage, in volts, across the 6 $$\Omega$$ resistor is ________. (round off to two decimal places).
GATE EE 2022
3
In the circuit, switch 'S' is in the closed position for a very long time. If the switch is opened at time t = 0, then iL (t) in amperes, for t ≥ 0 is
GATE EE 2021
4
The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules
transferred from the DC source until steady state condition is reached equals ______. (Give the
answer up to one decimal place.)
GATE EE 2017 Set 2
5
In the given circuit, the current supplied by the battery, in ampere, is ________.
GATE EE 2016 Set 1
6
A series RL circuit is excited at t = 0 by closing a switch as shown in the figure.
Assuming zero initial conditions, the value of $$\frac{\mathrm d^2\mathrm I}{\mathrm{dt}^2}$$ at t=0+ is 
GATE EE 2015 Set 2
7
The switch SW shown in the circuit is kept at position ‘1’ for a long duration. At t = 0+, the
switch is moved to position ‘2’ Assuming $$\left|V_{02}\right|\;>\;\left|V_{01}\right|$$, the voltage $$V_C\left(t\right)$$ across capacitor is
GATE EE 2014 Set 2
8
A combination of 1μF capacitor with an initial voltage Vc(0) = −2V in series with a 100Ω
resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0s
as shown. Which of the following graphs shown in the options approximates the voltage Vs
across the current source over the next few seconds?
GATE EE 2014 Set 1
9
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 EE 2012
10
The switch in the circuit has been closed for a long time. It is opened at t = 0. At
t = 0+, the current through the 1μF capacitor is
GATE EE 2010
11
In the Fig. given below, the initial capacitor voltage is zero. The switch is closed at $$t = 0.$$ the final steady-state voltage across the capacitor is
GATE EE 2005
12
A unit step voltage is applied at $$t = 0$$ to a series $$RL$$ circuit with zero initial conditions.
GATE EE 2001
13
In the series $$RC$$ circuit shown in Fig. the voltage across $$C$$ starts increasing when the $$d.c.$$ source is switched on. The rate of increase of voltage across $$C$$ at the instant just after the switch is closed (i.e., at $$t = {0^ + }$$), will be
GATE EE 1996
14
The time constant of the network shown in Fig. is
GATE EE 1992
15
In the circuit of Fig, the switch $$'S'$$ is closed at $$t=0$$ with $${i_L}\left( 0 \right) = 0$$ and $${V_C}\left( 0 \right) = 0.$$ In the steady state, $${V_C}$$ equals
GATE EE 1992
Marks 2
1
The circuit shown in the figure is initially in the steady state with the switch K in open condition and $$\overline K $$ in closed condition. The switch K is closed and $$\overline K $$ is opened simultaneously at the instant $$t=t_1$$, where $$t_1 > 0$$. The minimum value of $$t_1$$ in milliseconds, such that there is no transient in the voltage across the 100 $$\mu$$F capacitor, is ___________ (Round off to 2 decimal places).
GATE EE 2023
2
A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is 820 Ω, then the value C is ______ μF.
(Round off to 2 decimal places)
GATE EE 2021
3
A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at t = 0, and the capacitor voltage is found to cross 0 V at t = 0.4τ, where τ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at t = 0.2τ is _______ (rounded off to 2 decimal places).
GATE EE 2020
4
In the circuit shown, switch S2 has been closed for a long time. A time t = 0 switch S1 is closed. At
t=0+ , the rate of change of current through the inductor, in amperes per second, is _______.
GATE EE 2016 Set 1
5
In the Fig. shown, all elements used are ideal. For time t<0, S1 remained closed and S2 open. At t=0, S1 is opened and S2 is closed.If the voltage VC2 across the capacitor C2 at t = 0 is zero, the voltage across the capacitor combiation at t = 0+ will be
GATE EE 2009
6
The time constant for the given circuit will be
GATE EE 2008
7
In the circuit shown in Fig. switch $$S{w_1}$$ is initially CLOSED and $$S{w_2}$$ is OPEN. The inductor $$L$$ carries a current of $$10$$ $$A$$ and the capacitor is charged to $$10$$ $$V$$ with polarities as indicated. $$S{w_2}$$ in initially CLOSED at $$t = {0^ - }$$ and $$S{w_1}$$ is OPENED at $$t=0.$$ The current through $$C$$ and the voltage across $$L$$ at $$t = {0^ + }$$ is
GATE EE 2007
8
In the figure, transformer $${T_1}$$ has two secondaries, all three windings having the same number of turns and with polarities having the same number of turns and with polarities as indicated. One secondary is shorted by a $$10\,\Omega $$ resistor $$R,$$ and the other by a $$15\mu F$$ capacitor. The switch $$SW$$ is opened $$(t=0)$$ when the capacitor is charged to $$5$$ $$V$$ with the left plate as positive. At $$t=0+$$ the voltage $${V_P}$$ and current $${I_R}$$ are
GATE EE 2007
9
An ideal capacitor is charged to a voltage $${V_0}$$ and connected at $$t=0$$ across an ideal inductor $$L.$$ (The circuit now consists of a capacitor and inductor alone). If we let $${\omega _0} = 1/\sqrt {LC} ,$$ the voltage across the capacitor at time $$t>0$$ is given by
GATE EE 2006
10
A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it is moved to point $$2$$ at $$t = 0.$$
For the value of $$R$$ obtained in the above question, the time taken for $$95\% $$ of the stored energy to be dissipated is close to
GATE EE 2005
11
A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it is moved to point $$2$$ at $$t = 0.$$
If, at $$t = {0^ + }$$, the voltage across the coil is $$120$$ $$V,$$ the value of resistance $$R$$ is
GATE EE 2005
12
The circuit shown in the Fig. is in steady state, when the switch is closed at $$t=0.$$ Assuming that the inductance is ideal, the current through the inductor at $$t = {0^ + }$$ equals
GATE EE 2005
13
In figure, the capacitor initially has a charge of $$10$$ Coulomb. The current in the circuit one second after the switch $$S$$ is closed will be
GATE EE 2004
14
In the circuit shown in Fig., the switch $$S$$ is closed at time $$t=0$$. The voltage across the inductance at $$t = {0^ + },$$ is
GATE EE 2003
15
Consider the circuit shown in Fig. If the frequency of the source is $$50$$ $$Hz,$$ then a value of $${t_0}$$ which results in a transient free response is
GATE EE 2002
16
An $$11$$ $$V$$ pulse of $$10$$ $$µ$$s duration is applied to the circuit shown in Fig. Assuming that the capacitor is completely discharged prior to applying the pulse, the peak value of the capacitor voltage is
GATE EE 2002
17
A rectangular voltage pulse of magnitude $$V$$ and duration $$T$$ is applied to a series combination of resistance $$R$$ and capacitance $$C.$$ The maximum voltage developed across the capacitor is
GATE EE 1999
Marks 5
1
A constant current source is supplying $$10A$$ to a circuit shown in Fig. the switch $$S,$$ which is initially closed for a sufficiently long time, is suddenly opened. Obtain the differential equation governing the behaviour of the inductor current and hence obtain the complete time response of the inductor current. What is the energy stored in $$L,$$ a long time after the switch is opened?
GATE EE 2002
2
In the given circuit, the capacitor is initially charged to $$12$$ $$V. $$ Find the mathematical expression for the voltage across the capacitor $${{V_C}}$$ after closing the switch at $$t = 0.$$
GATE EE 1999
3
The switch in the following circuit, shown in Fig. has been connected to the $$12V$$ source for a long time. At $$t=0,$$ the switch is thrown to $$24$$ $$V$$.
$$L = 2\,H,\,\,{R_1} = 10\,\Omega ,\,\,{R_2} = 2\,\Omega ,\,\,C = 0.25\,\mu F$$
$$(a)$$ Determine $${i_L}\left( 0 \right)$$ and $${V_C}\left( 0 \right)$$
$$(b)$$ Write the differential equation governing $${V_C}\left( t \right)$$ for $$t>0$$
$$(c)$$ Compute the steady state value of $${V_C}\left( t \right)$$
GATE EE 1998
4
In the circuit shown in Fig., $${e_g}\left( t \right) = 2.5t$$ volts. What are the values of $$i(t)$$ and $${V_L}\left( t \right)$$ at $$t=4$$ seconds?
GATE EE 1997