# Sinusoidal Steady State Analysis · Electric Circuits · GATE EE

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## 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}$$reads$$12A$$and$${A_3}$$reads$$9A.{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,50Hz$$source draws, a current of$$10A.$$When t... GATE EE 1996 A coil (which can be modeled as a series$$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. ...
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