Ques 11. A current of i = 6 + 10sin(100π t) 20sin(200 π t) is flowing through a series combination of a PMMC and moving iron instrument. The ratio of the two currents as registered by the M.I. and PMMC meter is
1.81
3.11
2.82✔
2.63
i = 6 + 10sin(100π t) 20sin(200 π t)
PMMC read-only DC value
(I)PMMC = 6
For M.I instrument
Ques 12. Three resistance 5Ω each are connected in star, values of equivalent delta resistance are
1.5 Ω each
2.5 Ω each
5/3 Ω each
15 Ω each✔
If three resistance each of value R is connected in delta formation. Then the equivalent delta connection will have three resistance of equal value which is 3R.
In the above question, Individual resistance in Star connection = 5Ω
Individual resistance in Delta connection = 3 x 5 = 15Ω
Ques 13. A 120 V, 60 W incandescent lamp has to be operated from 220 V, 50c/s, 1 Phase AC supply. In order to do, this a circuit element has to be connected in series with the lamp. Which one of the following elements is preferable?
Pure Capacitance✔
Pure Inductance or capacitance
Resistance
Pure Inductance
Series capacitors are generally employed to improve the stability of the system and to increase the voltage rating.
We know that the reactance of a capacitor is given as
Rc = 1/2πfc
For an A.C. source, frequency, f > 0 i.e Rc = 1/2πfc > 0 which means that a capacitor offers a constant resistance in the A.C circuit i.e. it allows the lamp to glow continuously.
In the case of Inductance, the brightness of the lamp will depend upon the number of turns in the inductor
Ques 14. The bandwidth of an AC series circuit consisting of R, L and C is
L/R
R/2πL✔
L/RC
RC/L
Bandwidth is defined as the frequencies at which the power in the circuit is half of its maximum value.
The bandwidth of series RLC circuit
Bandwidth =(f2 – f1) = R/2πL
Where f1 is called lower half frequency
f2 is called as upper half frequency
Ques 15. For a balanced 3-phase supply system, the phasor sum of the line current is NOT zero if the load is
Balanced Delta connected
Unbalanced Delta connected
Balanced star connected
Unbalanced star connected✔
In the case of delta connection, whether the load is balanced or unbalanced the phasor sum of the line current is always zero.
But in the case of star connection, the phasor sum of the line current is not zero for unbalanced load but is equal to neutral current.
Ques 16. At series resonance of an RLC circuit, the impressed voltage is
Equal to the resistive drop✔
Equal to the capacity drop
Greater than the resistive drop
Equal to the inductive drop
At a particular frequency (resonant frequency), X1=X2 because resonance of a series RLC circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase. Thus, at the resonant frequency, the net reactance is zero because of X1=X2.
The circuit impedance Z becomes minimum and is equal to the resistance R. Impressed voltage is also called applied voltage therefore at a series resonance RLC circuit the impressed voltage or applied voltage is equal to the voltage across R.
Ques 17. In a series RLC circuit R 20Ω, XL = 30Ω, and Xc =30Ω. If the supply voltage across the combination is v = 100sin(100πt + 30° ) volts, the instantaneous current and the power factor of the circuit are respectively
I = 3.536 sin(100πt + 30° ) Amp, p.f =0.866
I = 5 sin(100πt + 30° ) Amps, p.f = unity✔
I = 3.536 sin(100πt + 30° ) Amps, p.f = unity
I = 5 sin(100πt + 30° ) Amps, p.f = 0.866
Given R = 20Ω
XL = 30Ω
Xc = 30Ω
At series RLC circuit
tanΦ = (XL – Xc)/R
= 30 – 30/20 = 0
or cosΦ =1
Impedance of RLC circuit
Z = 20Ω
I = V/Z
I = 100sin(100πt + 30° )/20
I = 5 sin(100πt + 30° ) Amp at unity power factor
Ques 18. The RMS of the alternating current given by the equation
i = 50 sin(314t – 10°) + 30 sin (314 t – 20°)
41.23 A✔
58.31 A
38.73 A
77. 43 A
RMS value of alternating current is given as
= 41.23 A
Ques 19. A series RLC circuit will have a unity P.F is operated at a frequency of
1/LC
LC
1/2π√LC✔
1/2LC
Series RLC circuit will have unity power factor when resonant will occur.
