# Sinusoidal Steady State Analysis · Electric Circuits · GATE EE

Start Practice## Marks 1

GATE EE 2022

An inductor having a Q-factor of 60 is connected in series with a capacitor having a Q-factor of 240. The overall Q-factor of the circuit is ________....

GATE EE 2022

The network shown below has a resonant frequency of 150 kHz and a bandwidth of 600 Hz. The Q-factor of the network is _______. (round off to nearest i...

GATE EE 2017 Set 2

The mean square value of the given periodic waveform f(t) is_________.
...

GATE EE 2015 Set 1

An inductor is connected in parallel with a capacitor as shown in the figure.
As the frequency of current i is increased, the impedance (Z) of the ne...

GATE EE 2015 Set 2

Find the transformer ratios a and b that the impedance (Zin) is resistive and equal 2.5 Ω
when the network is excited with a sine wave voltage of angu...

GATE EE 2012

The average power delivered to an impedance $$\left(4-j3\right)$$ Ω by a current $$5\cos\left(100\mathrm{πt}+100\right)\;A$$ is

GATE EE 2012

A two phase load draws the following phase currents:
$$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$,
$$i_2\left(t\right)=I_m\cos\le...

GATE EE 2011

The r.m.s value of the current i(t) in the circuit shown below is
...

GATE EE 2011

The voltage applied to a circuit is $$100\sqrt2\cos\left(100\mathrm{πt}\right)$$ volts and the circuit draws
a current of $$10\sqrt2\;\sin\left(100\ma...

GATE EE 2004

The value of $$Z$$ in Fig., which is most appropriate to cause parallel resonance at $$500$$ $$Hz$$ is
...

GATE EE 2001

In a series $$RLC$$ circuit at resonance, the magnitude of the voltage developed across the capacitor

GATE EE 1999

A series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and ha...

GATE EE 1999

The $$RMS$$ value of half $$-$$ wave rectified symmetrical square wave current of $$2A$$ is

GATE EE 1999

The current in the circuit shown in figure is
...

GATE EE 1998

A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$...

GATE EE 1998

A circuit with a resistor, inductor and capacitor in series is resonant at $${f_0}\,\,Hz.$$ If all the component values are now doubled, the new reson...

GATE EE 1996

In the circuit shown in Fig. $$X$$ $$-$$ is an element which always absorbs power. During a particular operation, it sets up a current of $$1$$ $$amp...

GATE EE 1995

A series $$R-L-C$$ circuit has the following parameter values:
$$R = 10\Omega ,\,\,L = 0.01\,H,\,\,C = 100\,\,m\,\,F.$$
The $$Q$$ factor of the circ...

GATE EE 1995

In the circuit of Figure, Ammeter $${A_2}$$ reads $$12$$ $$A$$ and $${A_3}$$ reads $$9$$ $$A.$$ $${A_1}$$ will read ______
...

GATE EE 1994

At resonance, the given parallel circuit constituted by an iron - cored coil and a capacitor behaves like
...

GATE EE 1993

In the following circuit (Fig.) $$i(t)$$ under steady state is
...

GATE EE 1993

The following circuit (Fig.) resonates at
...

## Marks 2

GATE EE 2019

A 0.1 μF capacitor charged to 100 V is discharged through a 1 kΩ resistor. The time in ms (round off to two decimal places) required for the voltage a...

GATE EE 2017 Set 2

In the circuit shown below, the value of capacitor C required for maximum power to be
transferred to the load is
...

GATE EE 2016 Set 1

In the circuit shown below, the supply voltage is 10sin(1000t) volts. The peak value of the steady
state current through the 1Ω resistor, in amperes, ...

GATE EE 2016 Set 1

The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the
admittance of the circuit becomes a pure conductance at all f...

GATE EE 2015 Set 1

The circuit shown in the figure has two sources connected in
series. The instantaneous voltage of the AC source (in volt) is
given by v(t) = 12sint. I...

GATE EE 2015 Set 2

In the given network $$V_1=100\angle0^\circ V$$, $$V_2=100\angle-120^\circ V$$, $$V_3=100\angle+120^\circ V$$. The phasor
current i (in Ampere) is
...

GATE EE 2015 Set 2

Two identical coils each having inductance L are placed together on the same core. If an
overall inductance of $$\alpha$$L is obtained by interconnect...

GATE EE 2015 Set 2

A symmetrical square wave of 50% duty cycle
has amplitude of ±15V and time period of 0.4$$\mathrm\pi$$
ms. This square wave is applied across a series...

GATE EE 2014 Set 3

A series RLC circuit is observed at two frequencies. At $$\omega_1$$ = 1k rad / s, we note that source
voltage $$V_1=100\angle0^\circ V$$ results in a...

GATE EE 2014 Set 2

The total power dissipated in the circuit, show in the figure, is 1kW.
The ideal voltmeter, across the load, reads 200 V. The value of XL is ________...

GATE EE 2014 Set 2

The voltage across the capacitor, as sown in the figure, is expressed as
$$$V_c\left(t\right)=A_1\sin\left(\omega_1t-\theta_1\right)+A_2\sin\left(\ome...

GATE EE 2013

Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the
chosen operating frequency. Their respective resistances are R1 and R2 . Wh...

GATE EE 2012

In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
The power factor of the load is...

GATE EE 2012

In the circuit shown, the three voltmeter readings are V1 = 220V, V2 = 122V , V3 = 136V.
If RL=5 Ω , the approximate power consumption in the load is...

GATE EE 2011

An RLC circuit with relevant data is given below.
The power dissipated in the resistor R is...

GATE EE 2011

An RLC circuit with relevant data is given below.
The current $${\underline I}_C$$ in the figure above is ...

GATE EE 2007

The $$R-L-C$$ series circuit shown is supplied from a variable frequency voltage source. The admittance $$-$$ locus of the $$R-L$$ $$-C$$ network at ...

GATE EE 2007

In the figure given below, all phasors are with reference to the potential at point $$''O''.$$ The locus of voltage phasor $${V_{YX}}$$ as $$R$$ is va...

GATE EE 2007

The resonant frequency for the given circuit will be
...

GATE EE 2006

The circuit shown in the figure is energized by a sinusoidal voltage source $${V_1}$$ at a frequency which causes resonance with a current of $${\rm I...

GATE EE 2005

The $$RL$$ circuit of the figure is fed from a constant magnitude, variable frequency sinusoidal voltage source $${V_{IN.}}$$ At $$100Hz,$$ the $$R$$...

GATE EE 2004

In Fig. the admittance values of the elements in Siemens are
$${Y_R} = 0.5 + j0,$$
$${Y_L} = 0 - j\,1.5,$$
$${Y_C} = 0 + j\,0.3$$ respectively.
Th...

GATE EE 2003

In the circuit of Fig. the magnitudes of $${V_L}$$ and $${V_C}$$ are twice that of $${V_R}$$. The inductance of the coil is
...

GATE EE 2002

In the circuit shown in Fig. what value of $$C$$ will cause a unity power factor at the $$ac$$ source?
...

GATE EE 2002

A series $$R-L-C$$ circuit has $$R = 50\Omega ;$$ $$L=100$$ $$\mu H$$ and $$C = 1\,\,\mu F.$$ The lower half power frequency of the circuit is

GATE EE 2002

A first order, low pass filter is given with $$R = 50\,\,\Omega $$ and $$C$$ $$ = 5\mu F.$$ What is the frequency at which the gain of the voltage tr...

GATE EE 2002

In the circuit shown in Fig. it is found that the input $$ac$$ voltage $$\left( {{V_i}} \right)$$ and current $$i$$ are in phase. The coupling coeffi...

GATE EE 2000

The impedance seen by the source in the circuit in Fig. is given by
...

GATE EE 2000

If an $$ac$$ voltage wave is corrupted with an arbitrary number of harmonics, then the overall voltage waveform differs from its fundamental frequency...

GATE EE 1999

A fixed capacitor of reactance –$$j0.02$$ $$\Omega $$ is connected in parallel across a series combination of a fixed inductor of reactance $$j0.01$$ ...

GATE EE 1999

The voltage phasor of a circuit is $$10\angle {15^0}\,V$$ and the current phasor is $$2\,\,\angle - {45^0}A.$$ The active and the reactive powers in ...

GATE EE 1997

Two identical coils of negligible resistance when connected in series across a $$200V,$$ $$50$$ $$Hz$$ source draws, a current of $$10$$ $$A.$$ When t...

GATE EE 1996

A coil (which can be modeled as a series $$RL$$ circuit) has been designed for high $$-$$ $$Q$$ performance at a rated voltage and a specified frequen...

GATE EE 1994

In the given circuit, the voltage $$\overline {{V_L}} $$ has a phase angle of ____________ with respect to $$\overline {{V_S}} .$$
...

## Marks 5

GATE EE 2001

Determine the resonance frequency and the $$Q$$ $$-$$ factor of the circuit shown in Fig.
Data: $$\,\,\,\,\,R = 10\,\Omega ,\,\,\,\,\,\,\,\,\,\,\,\...

GATE EE 1998

A circuit consisting of a single resistor $$R$$ and an inductor $$L$$ in series is driven by a $$25$$ $$V$$ $$rms,$$ $$50$$ $$Hz$$ sinusoidal voltage ...

GATE EE 1998

Determine the impedance seen by the source $${V_s} = 24\angle {0^0}$$ in the network shown in Fig.
...