Steady-State AC (EE)

The input voltage $v(t)$ and current $i(t)$ of a converter are given by, $v(t)=300 \sin (\omega t) \mathrm{V}$ $$ i(t)=10 \sin \left(\omega t-\frac{\pi}{6}\right)+2 \sin \left(3 \omega t+\frac{\pi}{6}\right)+\sin \left(5...

Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be improved to 0.85 pf lag. The line current of the capacitor bank, in $A$, is _________ (Round off to on...

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 ________. (round off to nearest integer).

A signal generator having a source resistance of $50 \Omega$ is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V...

A load is supplied by a $$230$$ $$V,$$ $$50$$ $$Hz$$ source. The active power $$P$$ and the reactive power $$Q$$ consumed by the load are such that $$1$$ $$kW$$ $$ \le P \le 2\,kW\,\,$$ and $$\,1\,\,kVAR \le 2\,\,kVAR.\,...

A three-phase cable is supplying $$800$$ kW and $$600$$ kVAr to an inductive load. It is intended to supply an additional resistive load of $$100$$ kW through the same cable without increasing the heat dissipation in the...

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 current $$I_1=0.03\angle31^\circ\;A$$. At $$\omega_2$$ = 2 k rad/s, t...

A single phase induction motor draws $$12MW$$ power at $$0.6$$ lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to $$0.8$$ lagging. As...

The complex power consumed by a constant-voltage load is given by $$\left( {{P_1} + {J_{q1}}} \right).\,\,$$ Where, $$\,1\,\,kW \le \,\,{P_1} \le \,\,\,1.5\,\,kW\,\,\,$$ and $$\,\,0.5\,KVAR \le \,\,\,{Q_1} \le 1kVAR.\,\,...

Two magnetically uncoupled inductive coils have Q factors q 1 and q 2 at the chosen operating frequency. Their respective resistances are R 1 and R 2 . When connected in series, their effective Q factor at the same opera...

A single load is supplied by a single voltage source. If the current flowing from the load to the source is $$10\angle - {150^0}$$ A and if the voltage at the load terminals is $$100\angle {60^0}$$ $$V,$$ then the

A two phase load draws the following phase currents: $$i_1\left(t\right)=I_m\sin\left(\omega t-\phi_1\right)$$, $$i_2\left(t\right)=I_m\cos\left(\omega t-\phi_2\right)$$. These currents are balanced if $$\phi_1$$ is equa...

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

The input voltage given to a converter is $${V_i} = 100\sqrt 2 \,\,\,\sin \,\,\,\left( {100\pi t} \right)\,\,V$$ The current drawn by the converter is $${i_i} = 10\sqrt 2 \,\,\,\sin \,\,\,\left( {100\pi t - {\pi \over 3}...

A lossy capacitor $${C_x}$$, rated for operation at $$5$$ $$kV,$$ $$50$$ $$Hz$$ is represented by an equivalent circuit with an ideal capacitor $${C_p}$$ in parallel with a resistor $${R_p}$$. The value $${C_p}$$ is foun...

The voltage applied to a circuit is $$100\sqrt2\cos\left(100\mathrm{πt}\right)$$ volts and the circuit draws a current of $$10\sqrt2\;\sin\left(100\mathrm{πt}+\mathrm\pi/4\right)$$ amperes. Taking the voltage as the refe...

Consider two buses connected by an impedance of $$\left( {0 + j5} \right)\Omega .$$ The bus $$1$$ voltage is $$100$$$$\angle {30^ \circ }\,\,\,V,$$ and bus $$2$$ voltage is $$100\angle {0^ \circ }\,\,\,V,$$ The real and...

The Thevenin's equivalent of a circuit operating at $$\omega = 5\,\,rad/s\,\,{V_{oc}} = 3.71\angle - {15.9^ \circ }$$ and $${Z_0} = 2.38 - j0.667\Omega .$$ At this frequency, the minimal realization of the Thevenin's ind...

A three phase balanced star connected voltage source with frequency $$\omega \,\,rad/s$$ is connected to a star connected balanced load which is purely inductive. The instantaneous line currents and phase to neutral volt...

$$230$$ $$V$$ (phase) $$50$$ Hz, three-phase, $$4$$-wire, system has a sequence $$ABC$$. A unity power-factor load of $$4$$ kW is connected between phase A and neutral $$N$$. It is desired to achieve zero neutral current...

A $$400$$ V, $$50$$ Hz, three phase balanced source supplies power to a star connected load whose rating is $$12\sqrt 3 $$ kVA, $$0.8$$ pf(lag). The rating (in kVAR) of the delta connected (capacitive) reactive power ban...

A $$400V$$, $$50$$ $$Hz,$$ three phase balanced source supplies power to a star connected load whose rating is $$12\,\,\angle 3\,\,kVA,$$ $$0.8$$ $$pf$$ (lag). The rating $$($$in $$kVAR)$$ of the delta connected (capacit...

At an industrial sub-station with a $$4$$ $$MW$$ load, a capacitor of $$2$$ MVAR is installed to maintain the load power factor at $$0.97$$ lagging. If the capacitor goes out of service, the load power factor becomes

Total instantaneous power supplied by a $$3$$-phase ac supply to a balanced $$R$$-$$L$$ load is

The rated voltage of a $$3$$-phase power system is given as

A balanced delta connected load of $$\left( {8 + j6} \right)$$ $$\Omega $$ per phase is connected to a $$400V,$$ $$50Hz,$$ $$3-$$ phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a...

A balanced delta connected load of $$\left( {8 + j6} \right)\Omega $$ per phase is connected to a $$400$$ $$V$$, $$50$$ $$Hz$$, $$3-$$phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecti...

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 transfer function of the filter is $$0.25?$$

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

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

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

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

A series $$R-L-C$$ circuit when excited by a $$10$$ $$V$$ sinusoidal voltage source of variable frequency, exhibits resonance at $$100$$ $$Hz$$ and has a $$3$$ $$dB$$ bandwidth of $$5$$ $$Hz.$$ The voltage across the ind...

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

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

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 the circuit are

A fixed capacitor of reactance –$$j0.02$$ $$\Omega $$ is connected in parallel across a series combination of a fixed inductor of reactance $$j0.01$$ $$\Omega $$ and a variable resistance $$R.$$ As $$R$$ is varied from z...

A 3-phase, 11 kV, 50 Hz, 200 kW load has a power factor of 0.8 lag. A delta connected 3-phase capacitor is used to improve the power factor to unity. The capacitance power phase of the capacitor in micro-farads is

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 source. A capacitor is to be placed in parallel with the source to imp...

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 resonant frequency is

A sinusoidal source of voltage $$V$$ and frequency $$f$$ is connected to a series circuit of variables resistance, $$R$$ and a fixed reactance, $$X.$$ The locus of the tip of the current phasor, $$I$$, as $$R$$ is varied...

Energy stored in a capacitor over a cycle, when excited by an $$a.c.$$ source is

A factory draws $$100$$ kW at $$0.7$$ p.f. lagging from a $$3$$-phase, $$11$$ kV supply. It is desired to the p.f. to $$0.95$$ lagging using series capacitors. Calculate the rating of the capacitor required.

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 frequency. If the frequency of operation is doubled, and the coil is operated...

A water boiler at home is switched on to the $$A.C$$ mains supplying power at $$230$$ $$V/50$$ $$Hz.$$ The frequency of instantaneous power consumed by the boiler is

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 circuit at resonance is