sinsusoidal steady state

8/10/2019 Sinsusoidal Steady State

1/13

Sinusoidal Steady State-MCQs

1. The value of current through the 1 Farad capacitor of figure is

AC 2 sin 100 t

1

1

1

1

2

1H

0.5F

0.5F

1F

(a) zero

(b) one

(c) two

(d) three[GATE 1987: 2 Marks]

Sol. The given circuit is a bridge circuit and can be redrawn as

AC 2+s a b

1+2/s

1F2 sin 100 t

The product of the opposite arms are equal

=

= = = + ( +) = The current through 1F capacitor is zero

Option (a)


2/13

2. The half power bandwidth of the resonant circuit of figure can be increased by:

R 2C

R 1

L

(a) increasing R 1 (b) decreasing R 1

(c) increasing R 2 (d) decreasing R 2

[GATE 1989: 2 Marks]

Sol. Bandwidth of the circuit

For increasing bandwidth, Q is to be decreased

= = If R 1 0, R 2, the circuit has only L & C elements and has high selectivity. , ,

Option (a) & (d)

3. The resonant frequency of the series circuit shown in figure is

M=1H

2H 2H 2F

(a) (b)

(c) (d)



3/13

Sol. The coils are connected in a series opposing way. As the current is entering thedot of coil L 1 and leaving the dot of coil L 2

= + = + =

At resonance X L = X C

=

= = = / =

Option (b)

4. In the series circuit shown in figure, for series resonance, the value of the couplingcoefficient k will be

18 -j12 j2 j8

K

(a) 0.25(b) 0.5

(c) 0.999(d) 1.0

[GATE 1993: 1 Mark]

Sol. The coils are connected in series additive manner as the current is entering thedot in both coils

= + + = = . =

At resonance | | = | |


4/13

= + + = + + +

At resonance = + = . = .

. = .

= = = .

Option (a)

5. In figure, A 1, A 2, and A 3 are ideal ammeters. If A 1 reads 5A, A 2 reads 12A, then A 3 should read

A 3

AC

A 2

A 1R

C

100 sin t

(a) 7 A(b) 12 A

(c) 13 A(d) 17 A


Sol. Since the source is a.c.

= + = + = =


5/13

Option (c)

6. A series LCR circuit consisting of = 10 ,| | = 20 | | = 20 is connectedacross an a.c. supply of 200 V rms. The rms voltage across the capacitor is(a) 200 90 (b) 200+90 (c)

400+90 (d) 400 90 [GATE 1994: 1 Mark]

Soln. For a series LCR circuit

= + = , =

= = = The voltage across the capacitor = . = . = =

Option (d)

7. A DC voltage source is connected across a series R-L-C circuit. Under steady stateconditions, the applied DC voltage drops entirely across the

(a) R only(b) L only

(c) C only(d) R and L combination

[GATE 1995: 1 Mark]

Soln. Under steady state condition, inductor behaves as a short circuit and capacitoras an open circuit.

The applied voltage drops entirely across the capacitor

R L C

Option (C)


6/13

8. Consider a DC voltage source connected to a series R-C circuit. When the steady statereaches, the ratio of the energy stored in the capacitor to the total energy supplied by thevoltage source, is equal to(a) 0.362(b) 0.500

(c) 0.632(d) 1.000

[GATE 1995: 1 Mark]

Soln. The total energy supplied by the source

= .

= =

= = Voltage across the uncharged capacitor

= Power in the capacitor =

= Energy stored in the capacitor at steady state

= [ ] =

= .


7/13

Option (b)

9. The current, i(t), through a 10- resistor in series with an inductance, is given by

i(t) = 3 + 4 sin (100 t + 450

) + 4 sin (300 t + 600

) amperes.The RMS value of the current and the power dissipated in the circuit are:

(a) 41A, 410 W, respectively(b) 35 A, 350 W, respectively

(c) 5 A, 250 W, respectively(d) 11 A, 1210 W respectively

[GATE 1995: 1 Mark]

Soln. = + ++ +

=

+ + =

Power dissipated = = =

Option (c)

10. In the circuit of Figure assume that the diodes are ideal and the meter is an averageindicating ammeter. The ammeter will read

A

4 sin ( t)Volts

D2

10 k

10 k

+

-

(a) 0.4 2 mA(b) 0.4 mA

(c) .8 (d) .

[GATE 1996: 1 Mark]


8/13

Soln. For positive half cycle of input D 1 is conducting and D 2 is off

The current through ammeter is the average value of positive half sine wave i.e.

= =

=

.

Option (d)

11. A series RLC circuit has a resonance frequency of 1 KHz and a quality factor Q = 100. Ifeach of R, L and C is doubled from its original value, the new Q of the circuit is

(a) 25

(b) 50

(c) 100

(d) 200[GATE 2003: 1 Mark]

Soln.

= =

=

=

When R, L and C are doubled = Option (b)

12. An input voltage = 10 2cos +10+10 5cos 2 + 10 V is applied to aseries combination of R = 1 and an inductance L = 1H. The resulting steady statecurrent i(t) in ampere is(a) 10cos +55+10cos 2 +10 +2 (b) 10cos +55+10 cos 2 +55 (c) 10cos 35+10cos 2 +10 2


9/13

(d) 10cos 35+10 cos 2 35 [GATE 2003: 2 Marks]

Soln.

= ++ +

= ++ + = , = Steady state current = +

= ++ + ++

= ++ + ++

= + + + = + + Option (C)

13. The circuit shown in the figure, with = , = , = 3 F has input voltage V(t) =Sin2t. The resulting current i(t) is

i(t)

V(t)R L C

(a) 5sin2 +53.1 (b) 5sin2 53.1 (c)

25sin2 +53.1 (d) 25sin2 53.1

[GATE 2003: 1 Mark]


10/13

Soln. Admittance

= + +

= + +

= + = +

= . = + = / = + . Option (a)

14. For the circuit shown in the figure, the time constant RC = 1 ms. The input voltage is

= 2sin10. The output voltage V 0 (t) is equal toR

vi(t) v0(t)

(a) sin10 45 (b) sin10 +45 (c)

sin10 53 (d) sin10 +53

[GATE 2004: 1 Mark]

Soln. = = / =


11/13

= +

= + = +

= + =

Option (a)

15. Consider the following statements S 1 and S 2 S1: At the resonant frequency the impedance of a series R-L-C circuit is zeroS2: In a parallel G-L-C circuit, increasing the conductance G results in increase in its Qfactor.Which one of the following is correct?

(a) S1 is FALSE and S 2 is TRUE(b) Both S 1 and S 2 are TRUE

(c) S1 is TRUE and S 2 is FALSE(d) Both S 1 and S 2 are FALSE


Soln. The impedance of a series RLC circuit at resonant frequency is

= + . = . At resonance

So, Z = R purely resistive

In a parallel RLC circuit,

3dB bandwidth =


12/13

= = =

is the resonant frequency.As conductance (As conductance G increases R reduces so Q reduces)Option (d)

16. An AC source of RMS voltage 20 V with internal impedance = 1+2 feeds aload of impedance = 7+4 in the figure below. The reactive power consumed bythe load is

DC

2 0 0 0 V

ZS = (1+2j)

Z L =

( 7 + 4 j )

(a) 8 VAR(b) 16 VAR

(c) 28 VAR(d) 32 VAR


Soln. The current I in the given circuit is

=

+ =

+

= + /

= . = .


13/13

Reactive power = = = 16 VAR

Option (b)

sinsusoidal steady state

Documents