Questions & Answers of Electric Circuits and Fields

•  (A)  R_A=R_B
•  (B)  R_A=R_B=0
•  (C)  R_A< R_B
•  (D)  R_B= R_A /(1+R_A)

•  (A)  $n_L$
•  (B)  $n^{2}L$
•  (C)  $\frac{n}{L}$
•  (D)  $\frac{n^2}{L}$

In the circuit shown below, the node voltage V_A is ___________ V.

•  (A)  65, 35 
•  (B)  50, 50
•  (C)  60, 90
•  (D)  60, 80

$v\left(t\right)=100\sin \left(\omega t\right)$ ,

$i\left(t\right)=10\sin \left(\omega t-{60}^{°}\right)+2\sin \left(3\omega t\right)+5\sin \left(5\omega t\right)$

The average power consumed by the load, in W, is___________.

•  (A)  0
•  (B)  5
•  (C)  10
•  (D)  20

•  (A)  2 and 5
•  (B)  5 and 2
•  (C)  3 and 4
•  (D)  4 and 3

The voltages developed across the 3 Ω and 2 Ω resistors shown in the figure are 6V and 2V respectively, with the polarity as marked. What is the power (in Watt) delivered by the 5V voltage source?

•  (A)  5
•  (B)  7
•  (C)  10
•  (D)  14

For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage,$V_{Th}$(in volt), seen from terminal AB is _________.

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 network varies as

•  (A) 
•  (B) 
•  (C) 
•  (D) 

The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?

•  (A)  416
•  (B)  440
•  (C)  200
•  (D)  920

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

In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-circuited. When 5 V is applied to Port1, a current of 1.25 A flows through a 1$\mathrm{\Omega }$ resistance connected across Port 2. When 3 V is applied to Port 1, then current (in Ampere) through a 2$\mathrm{\Omega }$ resistance connected across Port 2 is _________.

In the given circuit, the parameter k is positive, and the power dissipated in the 2$\mathrm{\Omega }$ resistor is 12.5 W. The value of k is________.

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 $\frac{{\mathrm{d}}^{2}i}{\mathrm{d}{t}^2}$ at t = $0^{+}$ is

•  (A)  $\frac{V}{L}$
•  (B)  $\frac{-V}{R}$
•  (C)  0
•  (D)  $\frac{-RV}{L^2}$

The current i (in Ampere) in the 2 $\mathrm{\Omega }$ resistor of the given network is ____ .

Find the transformer ratios a and b that the impedance (${\mathrm{Z}}_{in}$) is resistive and equal 2.5$\mathrm{\Omega }$ when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s.

•  (A)  a=0.5, b=2.0
•  (B)  a=2.0, b=0.5
•  (C)  a= 1.0, b=1.0
•  (D)  a=4.0, b=0.5

In the given network $V_1=100\angle 0^{°}$0°V, $V_2=100\angle -{120}^{°}$V, $V_3=100\angle +{120}^{°}$V. The phasor current i (in Ampere) is

•  (A)  173.2$\angle -{60}^{°}$
•  (B)  173.2$\angle {120}^{°}$
•  (C)  100.0$\angle -{60}^{°}$
•  (D)  100.0$\angle {120}^{°}$

Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $\alpha$L is obtained by interconnecting these two coils, the minimum value of $\alpha$ is ________.

The three circuit elements shown in the figure are part of an electric circuit. The total power absorbed by the three circuit elements in watts is __________.

C₀ is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If, half of the entire gap as shown in figure (b) is filled with a dielectric of permittivity ${\mathit{\in }}_r$, the expression for the modified capacitance is

•  (A) $\frac{C_0}{2}\left(1+{\in }_r\right)$
•  (B) $\left(C_0+{\in }_r\right)$
•  (C) $\frac{C_0}{2}{\in }_r$
•  (D) $C_0\left(1+{\in }_r\right)$

A combination of 1 µF capacitor with an initial voltage${\nu }_c\left(0\right)=-2\nu$ in series with a 100 O resistor is connected to a 20 mA ideal dc current source by operating both switches at t = 0 s as shown. Which of the following graphs shown in the options approximates the voltage v_s across the current source over the next few seconds?

•  (A) 
•  (B) 
•  (C) 
•  (D) 

An incandescent lamp is marked 40 W, 240V. If resistance at room temperature (26°C) is 120 Ω, and temperature coefficient of resistance is 4.5x10^-3/°C, then its ‘ON’ state filament temperature in °C is approximately _______

In the figure, the value of resistor R is (25 + I/2) ohms, where I is the current in amperes. The current I is ______

The following four vector fields are given in Cartesian co-ordinate system. The vector field which does not satisfy the property of magnetic flux density is

•  (A) $y^2{\mathbf{a}}_x+z^2{\mathbf{a}}_y+x^2{\mathbf{a}}_z$
•  (B) $z^2{\mathbf{a}}_x+x^2{\mathbf{a}}_y+x^2{\mathbf{a}}_z$
•  (C) $x^2{\mathbf{a}}_x+y^2{\mathbf{a}}_y+z^2{\mathbf{a}}_z$
•  (D) $y^2{z}^2{\mathbf{a}}_x+x^2{z}^2{\mathbf{a}}_y+z^2{y}^2{\mathbf{a}}_z$

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 380 μH and 240 μH. Their mutual inductance in μH is ________

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 |V_o2| > |V_o1|, the voltage v_c(t) across the capacitor is

•  (A) $v_c\left(t\right)=-V_{\mathrm{o}2}\left(1-e^{-t/2RC}\right)-V_{\mathrm{o}1}$
•  (B) $v_c\left(t\right)=V_{\mathrm{o2}}\left(1-e^{-t/2RC}\right)+V_{\mathrm{o1}}$
•  (C) $v_c\left(t\right)=-\left(V_{\mathrm{o2}}+V_{\mathrm{o1}}\right)\left(1-e^{-t/2RC}\right)-V_{\mathrm{o1}}$
•  (D) $v_c\left(t\right)=\left(V_{\mathrm{o2}}+V_{\mathrm{o1}}\right)\left(1-e^{-t/2RC}\right)+V_{\mathrm{o1}}$

A parallel plate capacitor consisting two dielectric materials is shown in the figure. The middle dielectric slab is placed symmetrically with respect to the plates.

If the potential difference between one of the plates and the nearest surface of dielectric interface is 2 Volts, then the ratio ε₁ : ε₂ is

•  (A) 1:4
•  (B) 2:3
•  (C) 3:2
•  (D) 4:1

Assuming an ideal transformer, the Thevenin’s equivalent voltage and impedance as seen from the terminals x and y for the circuit in figure are

•  (A) $2\sin \left(\omega t\right),4\Omega$
•  (B) $1\sin \left(\omega t\right),1\Omega$
•  (C) $1\sin \left(\omega t\right),2\Omega$
•  (D) $2\sin \left(\omega t\right),0.5\Omega$

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

$V_c\left(t\right)=A_1\sin \left({\omega }_{1}t-{\theta }_1\right)+A_2\sin \left({\omega }_{2}t-{\theta }_2\right)$

The values of  A ₁and  A ₂ respectively, are

•  (A) 2.0 and 1.98
•  (B) 2.0 and 4.20
•  (C) 2.5 and 3.50
•  (D) 5.0 and 6.40

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  X_L is ___________.

The magnitude of magnetic flux density $\left(\overrightarrow B\right)$ at a point having normal distanced meters from an infinitely extended wire carrying current of I A is$\frac{{\mu }_{0}I}{2\pi d}$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. ${\mu }_0$ is permeability of free space. Assume $\widehat i$, $\widehat j$, $\widehat k$ to be unit vectors along x, y and z axes respectively

Assuming right handed coordinate system, magnetic field intensity, $\overrightarrow H$ at coordinate (2,1,0) will be

•  (A) $\frac3{2\mathrm\pi}\widehat K\;weber/m^2$
•  (B) $\frac4{3\mathrm\pi}\widehat i\;A/m$
•  (C) $\frac4{3\mathrm\pi}\widehat i\;A/m$
•  (D) $\frac3{2\mathrm\pi}\widehat K\;A/m$

The line A to neutral voltage is A10∠15^oV for a balanced three phase star-connected load with phase sequence ABC. The voltage of line B with respect to line C is given by

•  (A) $10\sqrt{3}\angle 105°V$
•  (B) $10\angle 105°V$
•  (C) $10\sqrt{3}\angle -75°V$
•  (D) $-10\sqrt{3}\angle 90°V$

The driving point impedance Z(s) for the circuit shown below is

•  (A) $\frac{s^4+3s^2+1}{s^3+2s}$
•  (B) $\frac{s^4+2s^2+4}{s^2+2}$
•  (C) $\frac{s^2+1}{s^4+s^2+1}$
•  (D) $\frac{s^3+1}{s^4+s^2+1}$

A non-ideal voltage source V_s has an internal impedance of Z_s. If a purely resistive load is to be chosen that maximizes the power transferred to the load, its value must be

•  (A) 0
•  (B) real part of Z_s
•  (C) magnitude of Z_s
•  (D) complex conjugate of Z_s

The Norton’s equivalent source in amperes as seen into the terminals X and Y is _______.

The power delivered by the current source, in the figure, is ________.

A series RLC circuit is observed at two frequencies. At ω₁=1 krad/s, we note that source voltage $V_1=100\angle 0^{o}V$ results in a current $I_1=0.03\angle {31}^{o}A$. At ${\omega }_2=2$ krad/s, the source voltage $V_2=100\angle 0^{o}V$ results in a current $I_1=2\angle {31}^{o}A$. The closest values for R,L,C out of the following options are

•  (A) R=50 Ω;L =25 mH;C=10 μF;
•  (B) R=50 Ω;L =10 mH;C=25 μF;
•  (C) R=50 Ω;L =50 mH;C=5 μF;
•  (D) R=50 Ω;L =5 mH;C=50 μF;

A source ${\nu }_s\left(t\right)=V\cos 100\pi t$ has an internal impedance of $(4+j3)\mathrm{\Omega }$.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

•  (A) 3
•  (B) 4
•  (C) 5
•  (D) 7

The flux density at a point in space is given by $\mathbf{B}\mathbf{=}4x{\mathbf{a}}_{\mathrm{x}}+2ky{\mathbf{a}}_{\mathbf{y}}+8{\mathbf{a}}_{\mathbf{z}}$ Wb/m². The value of constant k must be equal to

•  (A) -2
•  (B) -0.5
•  (C) +0.5
•  (D) +2

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k > 0, the elements of the corresponding star equivalent will be scaled by a factor of

•  (A) $k^2$
•  (B) $k$
•  (C) $1/k$
•  (D) $\sqrt{k}$

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 R_L is

•  (A) $100\angle 90°$
•  (B) $800\angle 0°$
•  (C) $800\angle 90°$
•  (D) $100\angle 60°$

Three capacitors C₁, C₂, and C₃, whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown, the maximum safe voltage in Volts that can be applied across the combination and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively

•  (A) 2.8 and 36
•  (B) 7 and 119
•  (C) 2.8 and 32
•  (D) 7 and 80

Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

•  (A) q₁R₁+q₂R₂
•  (B) q₁/R₁+q₂/R₂
•  (C) (q₁R₁+q₂R₂)/(R₁+R₂)
•  (D) q₁R₂+q₂R₁

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage V_WX1 = 100V is applied across WX to get an open circuit voltage V_YZ1  across YZ. Next, an ac voltage V_YZ2  = 100V is applied across YZ to get an open circuit voltage V_WX2  across WX. Then, V_YZ1/V_WX1,V_WX2/V_YZ2 are respectively,

•  (A) 125/100 and 80/100
•  (B) 100/100 and 80/100
•  (C) 100/100 and 100/100
•  (D) 80/100 and 80/100

In the circuit shown below, the current through the inductor is

•  (A) $\frac{2}{1+j}A$
•  (B) $\frac{-1}{1+j}A$
•  (C) $\frac{1}{1+j}A$
•  (D) 0

The impedance looking into nodes 1 and 2 in the given circuit is

•  (A) 50$\Omega$
•  (B) 100$\Omega$
•  (C) 5 k$\Omega$
•  (D) 10.1 k$\Omega$

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 equal to

•  (A) $-{\Phi }_2$
•  (B) ${\Phi }_2$
•  (C) $\left(\mathrm{\pi }/2-{\Phi }_2\right)$
•  (D) $\left(\mathrm{\pi }/2+{\Phi }_2\right)$

The average power delivered to an impedance (4-j3)$\Omega$ by a current $5\cos \left(100\pi t+100\right)A$ is

•  (A) 44.2 W
•  (B) 50 W
•  (C) 62.5 W
•  (D) 125 W

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

•  (A) zero
•  (B) a step function
•  (C) an exponentially decaying function
•  (D) an impulse function

If V_A-V_B=6V, then V_C-V_D is

•  (A) –5 V
•  (B) 2 V
•  (C) 3 V
•  (D) 6 V

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

•  (A) 0.8$\Omega$
•  (B) 1.4$\Omega$
•  (C) 2$\Omega$
•  (D) 2.8$\Omega$

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1Ω$$ connected at port B draws a current of 3 A
(ii) 2.5Ω$$ connected at port B draws a current of 2 A

For the same network, with 6 V dc connected at port A, 1Ω connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is

•  (A) 6 V
•  (B) 7 V
•  (C) 8 V
•  (D) 9 V

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1Ω$$ connected at port B draws a current of 3 A
(ii) 2.5Ω$$ connected at port B draws a current of 2 A

With 10 V dc connected at port A, the current drawn by 7Ω connected at port B is

•  (A) 3/7 A
•  (B) 5/7 A
•  (C) 1 A
•  (D) 9/7 A

In the circuit shown, the three voltmeter readings are V₁=220V , V₂=122V , V₃=136V .

The power factor of the load is

•  (A) 0.45
•  (B) 0.50
•  (C) 0.55
•  (D) 0.60

In the circuit shown, the three voltmeter readings are V₁=220V , V₂=122V , V₃=136V .

If R_L=5Ω, the approximate power consumption in the load is

•  (A) 700 W
•  (B) 750 W
•  (C) 800 W
•  (D) 850 W