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651.

A long conducting wire `AH` is moved over a conducting triangular wire `CDE` with a constant velocity `v` in a uniform magnetic field `vec(B)` directed into the plane of the paper. Resistance per unit length of each wire is `rho`. Then A. a constant clockwise induced current will flow in closed loopB. an increasing anticlockwise indiced current will flow in the closed loopC. a decreasing anticlockwise induced current will flow in the closed loopD. a constant anticlockwise induced current will flow in the closed loop

Answer» Correct Answer - D
652.

The radius of the circular conducting loop shown in is R. magnetic field is decreasing at a constant rate `alpha`. Resisitance per unit length of the loop is `rho`. Then, the current in wire `AB` is (`AB` is one of the diameters) A. `(Ralpha)/(2rho)"from Ato"B `B. `(Ralpha)/(2rho)"fromBtoA" `C. `(2Ralpha)/(rho)"fromAtoB" `D. zero

Answer» Correct Answer - D
653.

Assertion : When a current flows in the coil of a transformer then its core becomes hot. Reason : The core of transformer is made of softiron.A. If both assertion ans reason are true ans reaason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation of assertion.C. If assertion istrue but reason is false.D. If both assertion and reason are false.

Answer» Correct Answer - B
When alternating current flows through the coil of a transformer, the core of transormer is magnetised and demagnetised repeatedly. The electrical energy taken by the core during magnetisation is not returned fully in demagnetisation. The energy remaining in the core appears in the from of heat.
654.

For the series `LCR` circuit shown in the figure, what is the resonance frequency and the amplitude of the current at the resonating frequency A. `2500 rad-s^(-1)` and `5sqrt(2) A`B. `2500 rad-s^(-1)` and `5 A`C. `2500 rad-s^(-1)` and `5/sqrt(2) A`D. `25 rad-s^(-1)` and `5sqrt(2) A`

Answer» Correct Answer - b
655.

In an A.C. circuit the currentA. Always leads the voltageB. Always lags behind the voltageC. Is always in phase with the voltageD. May lead or lag behind or be in phase with the voltage

Answer» Correct Answer - d
656.

In a series L-C-R circuit shown in the figure , what is the resonance frequency and the current at the resonating frequency?A. `0^(@)`B. `30^(@)`C. `45^(@)`D. `60^(@)`

Answer» Correct Answer - A
a) Impedance,
`Z=sqrt(R^(2)+(X_(L)-X_(C))^(2)`
`10=sqrt((10^(2)+(X_(L)-X-( C))^(2)`
`rArr 100 = 100+(X_(L)-X_(C))^(2)`
`rArr X_(L)-X_(C)=0`…………(i)
Let `phi` is the phase difference between current and voltage
`therefore tanphi = (X_(L)-X_(C))/R`
`therefore tanphi=0/R`
`phi=0` [From Eq. (i)]`
657.

The electric current in an `AC` circuit is given by `I=I_(0)sin omegat`.What is the time taken by the current to change from its maximum value to the `rms` value?

Answer» Correct Answer - `T//8` or `pi/(4omega)`
`I_(1)=I_(0)sin omega t_(1)`
`I_(0)=I_(0)sin omega t_(1)`
`t_(1)=(pi//2)/(2pi//T)=T/4`
& `I_(2)=I_(0)/sqrt2=I_(0) sin (omega t_(2))`
`t_(2)=(pi//4)/(2pi//T)=T/8`
`Deltat=t_(1)-t_(2)=T/4-T/8=T/8`
658.

The efficiency of a transformer is 98%. The primary voltage and current are`200 V` and `6A`. If the secondary voltage is `100 V`, the secondary currentA. `11.76 A`B. `12.25 A`C. `3.06 A`D. `2.94 A`

Answer» Correct Answer - 3
`eta = (V_(s) I_(s))/(V_(p) I_(p)) implies (98)/(1000) = (100 xx i)/(200 xx 6)`
659.

Choke coil is a seriesA. L-R circuit with low L and high RB. L-R circuit with high L and low RC. C-R circuit with low C and high RD. C-R circuit with high C and low R

Answer» Correct Answer - B
660.

In problem No. 1, when switch is shifted from position A to B, what is the time period of resulting charge oscillation ?A. `(2pi)/(sqrt(LC))`B. `pisqrt((L)/(C))`C. `2pisqrt(LC)`D. `2pisqrt((L)/(C))`

Answer» Correct Answer - C
661.

Voltage input in a circuit is V = 300 `sin (omega t)` with current = 100 `cos(omega t)` . Average power loss in the circuit isA. 3000 unitsB. 1500 unitsC. 1000 unitsD. Zero

Answer» Correct Answer - D
662.

Which of these have dimension, different from others ?A. `(1)/(RC)`B. `(R)/(L)`C. `(1)/(sqrt(LC))`D. `(C)/(L)`

Answer» Correct Answer - D
663.

For which set of values of `X_(L), X_(C) and R`, a series LCR circuit will be in resonance ?A. `X_(L)=10 Omega, X_(C)=5 Omega, R = 10 Omega`B. `X_(L)=5 Omega, X_(C)=10Omega, R = 10 Omega`C. `X_(L) = 10 Omega, X_(C)= 10 Omega, R = 5 Omega`D. `X_(L) = 5 Omega, X_(C) = 3 Omega, R = 4 Omega`

Answer» Correct Answer - C
664.

Assertion: At resonance, power factor of L-C-R series circuit is 1. Reason: At resonance, `X_(C) = X_(L)`A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.C. If Assertion is true but Reason is false.D. If Assertion is false but Reason is true.

Answer» Correct Answer - A
At resonance, `X_(C)=X_(L)` and Z=R
`therefore` Power factor, `cosphi = R/Z=1`
665.

The `i - v` curve for anti-resonant circuit isA. B. C. D.

Answer» Correct Answer - b
666.

The resonance point in `X_(L) - f` and `X_(C ) - f` curves is A. PB. QC. RD. S

Answer» Correct Answer - c
667.

The vector diagram of current and voltage for a circuit as shown. The components of the circuit will be A. LCRB. LRC. LCR ot LRD. None of these

Answer» Correct Answer - c
668.

In pure inductive circuit, the curves between frequency `f` and reciprocal of inductive reactance `1//X_(L)` isA. B. C. D.

Answer» Correct Answer - c
669.

Which of the following graphs represent the correct variation of inductive reactance `X_(L)` with frequency `upsilon`?A. B. C. D.

Answer» Correct Answer - B
Inductive reactance,
`X_(L)=omega L = 2pi upsilon L rArr X_(L) prop upsilon`
Hence, unductive reactance increases linearly with frequency.
670.

In pure inductive circuit, the curves between frequency `f` and reciprocal of inductive reactance `1//X_(L)` isA. B. C. D.

Answer» Correct Answer - C
`X_(L)=2pifLimplies X_(L) prop fimplies 1/(X_(L)) prop 1/f`
i.e. graph between `1/(X_(L))` and `f` will be a hyperbola.
671.

A bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased, while keeping the voltage of the source constant, thenA. Bulb will give more intense lightB. Bulb will give less intense lightC. Bulb will give light of same intensity as beforeD. Bulb will stop radiating light

Answer» Correct Answer - A
When a bulb and a capacitor are connected in series to an AC source, then on increasing the frequency the current in the circuit is increased, because the impedence of the circuit is decreased. So the bulb will give more intense light.
672.

A series LCR circuit containing a resistance of `120 Omega` has angular resonance frequency `4 xx 10^(5) rad s^(-1)`. At resonance the vlotage across resistance and inductance are 60V and 40 V, repectively, the value of inductance L isA. `0.1 mH`B. `0.2 mH`C. `0.35 mH`D. `0.4 mH`

Answer» Correct Answer - B
At resonance as `X=0, I+V/R =60/120 = 1/2 A`
as `V_(L) = IX_(L) = I omega L, L+(V_L)/(I omega)`
so, ` L+(40)/((1//2)xx4xx(10^5))=0.2 mH`
i.e. `C=(1)/(0.2 xx 10^(-3) xx (4 xx 10^(5))^(2))=(1)/(32 (mu)F`.
Now in case of series LCR circuit.
` tan(phi)=(X_(L)-X_(C ))/(R )`
So current will lag the applied voltage by `45^(@)` if ,
`tan 45^(@) =(omega L -(1)/(omega L))/(R )`
` 1 xx 120 = omega xx 2 xx 10^(-4)-(1)/(omega (1//32)xx10^(-6))`
`omega^(2) - 6 xx 10^(5) omega - 16 xx 10^(10)=0`
i.e. `omega = (6 xx(10^5) +- sqrt((6 xx 10^(5))^(2)+64 xx 10^(10)))/(2)`
i.e., `omega = (6 xx (10^5) + 10 xx (10^5))/(2) = 8 xx 10^(5) rad s ^(-1)`.
673.

An ac ammeter is used to measure currnet in a circuit. When a given direct current passes through the circuit. The ac ammeter reads 3 A. When another alternating current passes through the circuit, the ac ammeter reads 4A. Then find the reading of this ammeter (inA), if dc and ac flow through the circuit simultaneously.

Answer» Correct Answer - 5
Ar an instant current in the circuit is
`i=3+4sqrt2 sin omegat`
Reading of ammeter is `lt i gt =sqrt((1)/(T)int_(0)^(T)i^(2)dt)`
674.

In a pure capacitive circuit if the frequency of ac source is doubled, then its capacitive reactance will beA. remains sameB. doubledC. halvedD. zero

Answer» Correct Answer - C
Capacitive reactance, `X_(C )=(1)/(2pi upsilon C)`
`rArr X_(C ) prop (1)/(upsilon) therefore (X_(C_(1)))/(X_(C_(2)))=(upsilon_(2))/(upsilon_(1))=(2upsilon)/(upsilon)=2`
`rArr X_(C_(2)) = (X_(C_(1)))/(2)`
675.

With increase in frequency of an `AC` supply, the capacitive reactance:A. varies inversely with frequencyB. varies directly with frequencyC. varies directly as square of frequenyD. remains constant

Answer» Correct Answer - A
676.

In an `a.c.` circuit consisting of resistance `R` and inductance `L`, the voltage across `R` is `60` volt and that across `L` is `80` volt.The total voltage across the combination isA. `140 V`B. `20 V`C. `100 V`D. `70 V`

Answer» Correct Answer - C
677.

An ac ammeter is used to measure currnet in a circuit. When a given direct current passes through the circuit. The ac ammeter reads 3 A. When another alternating current passes through the circuit, the ac ammeter reads 4A. Then find the reading of this ammeter (inA), if dc and ac flow through the circuit simultaneously.A. `3 A`B. `4 A`C. `7 A`D. `5 A`

Answer» Correct Answer - D
678.

A series combination of resistor (R), capacitor (C) is connected to an AC source of angular frequency `omega`. Keeping the voltage same, If the frequency is changed to `Omega/3`, the current becomes half of the original current. Then, the ratio of the capacitance reactance and resistance at the former frequency isA. `sqrt(0.6)`B. `sqrt(3)`C. `sqrt(2)`D. `sqrt(6)`

Answer» Correct Answer - A
`I_(rms) = V_(rms)/(sqrt(R^(2) + (1/(omegaC))^(2)))`...........(i)
`I_(rms)/2= V_(rms)/(sqrt(R^(2)+[(1/((omegaC)//3))]^(2)))= V_(rms)/sqrt(R^(2)+9/(omega^(2)C^(2)))`..........(ii)
From eqs. (i) and (ii), we get
`3R^(2)= 5/(omega^(2)C^(2))`
`1/(omegaC//R)=sqrt(3/5)`
or `X_(C)/R = sqrt(3/5)` or `X_(C)/R = sqrt(0.6)`
679.

If both the resistance and the inductance in an LR AC series circuit are doubled the new impedance will beA. halvedB. fourfoldC. doubledD. quadrupted

Answer» Correct Answer - C
For L-R circuit, `Z = sqrt(R^(2)+L^(2))`
Hence, `Z_(1) = sqrt(R^(2)+X_(L)^(2))`
Here, `Z_(1) = sqrt((R_(1)^(2)) + (X_(L_(2)))^(2))`
and `Z_(2) = sqrt((R_(2))^(2) + (X_(L2))^(2))`
Given, `R_(2)` = 2R and `X_(L2)= 2X_(L)`
`Z_(2) = sqrt((2r)^(2)+(2X_(L))^(2) = 2Z_(1)`
680.

The correct variation of resistance `R` with frequency `f` is given byA. B. C. D.

Answer» Correct Answer - 1
681.

The emf and current in a circuit are such that `E = E_(0) sin omega t` and `I - I_(0) sin (omega t - theta)`. This `AC` circuit containsA. `R` and `L`B. `R` and `C`C. only `R`D. only `C`

Answer» Correct Answer - 1
682.

The rms value of the emf given by ` E = 8 sin omegat + 6 sin 2omegat` .A. `5sqrt2 V`B. `7sqrt2 V`C. `10V`D. `10sqrt2V`

Answer» Correct Answer - A
`barE^(2) = 8^(2)/(2) + 6^(2)/(2) = 50 `
`E_(rms) = sqrt(barE^(2)) = 5 sqrt2 V` .
683.

An AC is given by the equation `i=i_(1)cos omegat+i_(2)sin omegat`. The r.m.s. current is given byA. `(i_(1) + i_(2))/(sqrt2`B. `(|i_(1) + i_(2)|)/(sqrt2`C. `sqrt((i_(1) + i_(2))/(2`D. `sqrt((i_(1) + i_(2))/(sqrt2`

Answer» Correct Answer - C
`bari^(2) = (i_(1)^(2))/(2) + i_(2)^(2)/(2)`
`i_(rms) = sqrt((bari_(1)^(2)+ i_(2)^(2))/(2)` .
684.

The magnitude inducted e.m.f. in an `LR` circuit at brea of circuit as compared to its value at make of circuit will beA. lessB. moreC. some times less and some times moreD. nothing can be said

Answer» Correct Answer - 2
685.

An AC is given by the equation `i=i_(1)cos omegat+i_(2)sin omegat`. The r.m.s. current is given byA. `1/sqrt(2) (i_(1)+i_(2))`B. `1/sqrt(2) (i_(1)+i_(2))^(2)`C. `1/sqrt(2) (i_(1)^(2)+i_(2)^(2))^(1//2)`D. `1/2 (i_(1)^(2)+i_(2)^(2))^(1//2)`

Answer» Correct Answer - c
686.

In general in an alternating current circuitA. The average value of current is zeroB. The average value of square of the current is zeroC. Average power dissipation is zeroD. The phase difference between voltage and current is zero

Answer» Correct Answer - a
687.

An AC generator produced an output voltage `E=170sin 377t` volts , where `t` is in seconds. The frequnecy of `AC` voltage isA. 50 HzB. 110 HzC. 60 HzD. 230 Hz

Answer» Correct Answer - c
688.

Maximum efficiency of a transformer depends onA. the working condtitions of technicians.B. weather copper loss `= 1//2 x` irons lossC. weather copper loss = iron lossD. weather copper loss `= 2 x` iron loss

Answer» Correct Answer - 3
689.

For an LCR series circuit with an aac source of angular frequency `omega`.A. circuit will be capacitive if `omega(1)/(sqrt(LC))`B. circuit will be inductive if `omega=(1)/(sqrtLC)`C. power factor of circuit will by capacitive reactance equals incductive reactance.D. current will be leading voltage is if `omega gt (1)/(sqrtLC)`

Answer» Correct Answer - C
690.

For an LCR series circuit with an aac source of angular frequency `omega`.A. circuit will be capactive if `omega gt (1)/(sqrt(LC))`B. circuit will be inductive if `omega = (1)/(sqrt(LC))`C. power factor of circuit will be unity of capacitive reactance equal inductive reactanceD. current will be leading voltage if `omega gt (1)/(sqrt(LC))`

Answer» Correct Answer - 3
691.

A light bulb has the rating 200 W 220 V. Find the peak value of current.

Answer» Correct Answer - `(10)/(11)sqrt(2)=1.3 A`
692.

Assertion: In series, L-C-R voltage across capacitor is always less than the applied voltage. Reason: In series L-C-R circuit, `V = sqrt((V^(2) + (V_(L)^(2)-V_(C)^(2)))`A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.C. If Assertion is true but Reason is false.D. If Assertion is false but Reason is true.

Answer» Correct Answer - D
d) `V_(R) larrV`, but `V_(C)` or `V_(L)` can be greater than V also.
693.

A lamp is connected in series with a capacitor. Predict your observations for dc and ac connections. What happens in each case if capacitance of the capacitor is reduced?

Answer» When a dc source is connected to a capacitor, the capacitor gets charged and after charging no current flows in the circuit and the lamp will not glow. There will be no change even if C is reduced. With ac source, the capacitor offers capacitative reactance `(1//omegaC)` and the current flows in the circuit. Consequently, the lamp will shine. Reducing C will increase reactance and the lamp will shine less brightly than before.
694.

If the frequency of applied source is increased, how will brightness change?

Answer» Correct Answer - Brightness will decrease
695.

In the circuit, shown in fig. what will be the effect on the brightness of blub if frequency of the source `omega` is increased?

Answer» `Z sqrt(R^(2)+(1)/((omega C)^(2)))` decreases on increasing w. This increases current. Hence the Brightness will increases.
696.

In the above question, what will be the effect on the brightness of bulb if frequency of the source `omega` is increased?

Answer» the brightmess will decreases, because Z increases on increasing w.
697.

If number of turns in the coil is increased, how will brightness change ?

Answer» Correct Answer - Decreases
698.

For the circuit shown in figureure, find the instaneous current through each element. .

Answer» The three current equations are,
`V=I_(R)R, V=L(dI)_(L))/(dt)` and `(dV)/(dt) = 1/CI_(C)`.............(i)
The steady state solutions of Eq. (i) are, `I_(R) = V_(0)/Rsinomegat-=(I_(0))_(R)sinomegat`
`I_(L) = -V_(0)/(omegaL) cosomegat=V_(0)/X_(L)cosomegat-=-(I_(0))_(L)cosomegat`
and `I_(C)=V_(0)omegaCcosomegat =V_(0)/X_(C) cosomegat-=(I_(0))_(C) cosomegat`............(ii)
where, the reactance `X_(L)` and `X_(C)` are as defined.
699.

Assertion: A capacitor is not connected in a DC circuit. Reason: In DC circuit, current through capacitor circuit becomes zero in stady state.A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.C. If Assertion is true but Reason is false.D. If Assertion is false but Reason is true.

Answer» Correct Answer - D
d) Capacitance is connected in DC circuit for charging of capacitor.
700.

A light bulb has the rating 200 W 220 V. If the supply voltage is 200 V, then find power consumed by the bulb.

Answer» Correct Answer - `P(V^(2))/(R)=(200xx200)/(242)=165` Watt