# GATE Questions & Answers of Sinusoidal Steady-State Analysis

## What is the Weightage of Sinusoidal Steady-State Analysis in GATE Exam?

Total 13 Questions have been asked from Sinusoidal Steady-State Analysis topic of Electric Circuits subject in previous GATE papers. Average marks 1.85.

In the figure, the voltages are $v_1(t)=100\cos\left(wt\right),\;v_2(t)=100\cos\left(wt+\mathrm\pi18\right)\;\;$ and $v_3(t)=100\cos\left(wt+\mathrm\pi36\right)$. The circuit is in sinusoidal steady state, and $R<<wL.P_1,P_2\;$ and $P_3$ are the average power outputs. Which one of the following statements is true?

The equivalent impedance $Z_{eq}$ for the infinite ladder circuit shown in the figure is

The voltage across the circuit in the figure, and the current through it, are given by the following expressions

$v(t)=5-10\;\cos\left(wt+60^\circ\right) V$

$i(t)=5+X\;\cos\left(wt\right)A$

where $w=100\mathrm\pi$ radian/s. If the average power delivered to the circuit is zero, then the value of $\mathrm X$ (in Ampere) is _____ (up to 2 decimal places).

The voltage $v(t)$ across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency $w=100$radian/s. When the inductor current $i(t)$ is in phase with the voltage $v(t)$, the magnitude of the impedance Z (in $\mathrm\Omega$) seen between the terminals a and b is ________ (up to 2 decimal places).

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $V_{an}=220\;\sin\left(100\;\mathrm{πt}\right)\;V$ and $i_a=10\;\sin\left(100\;\mathrm{πt}\right)\;A,$ respectively. Similarly for phase-b, the instantaneous voltage and current are $V_{bn}=220\;\cos\left(100\;\mathrm{πt}\right)\;V$ and $i_b=10\;\cos\left(100\;\mathrm{πt}\right)\;A,$, respectively.

The total instantaneous power flowing from the source to the load is

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) = 12 sin t. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ______.

In the given network V, ${V}_{2}=100\angle -{120}^{°}$V, ${V}_{3}=100\angle +{120}^{°}$V. The phasor current i (in Ampere) is

A symmetrical square wave of 50% duty cycle has amplitude of ±15 V and time period of 0.4π ms. This square wave is applied across a series RLC circuit with R = 5$\mathrm{\Omega }$, L = 10 mH, and C = 4μF. The amplitude of the 5000 rad/s component of the capacitor voltage (in Volt) is __________.

The voltage across the capacitor, as shown in the figure, is expressed as

${V}_{c}\left(t\right)={A}_{1}\mathrm{sin}\left({\omega }_{1}t-{\theta }_{1}\right)+{A}_{2}\mathrm{sin}\left({\omega }_{2}t-{\theta }_{2}\right)$

The values of  A 1and  A 2 respectively, are

The total power dissipated in the circuit, shown in the figure, is 1 kW.

The voltmeter, across the load, reads 200 V. The value of  XL is ___________.

A source ${\nu }_{s}\left(t\right)=V\mathrm{cos}100\pi t$ has an internal impedance of $\left(4+j3\right)\mathrm{\Omega }$.If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\mathrm{\Omega }$ should be

In the circuit shown below, if the source voltage ${V}_{s}=100\angle 53.13°\mathrm{V}$ then Thevenin’s equivalent voltage in Volts as seen by the load resistance RL is