MCQ

MCQ 1011 Mark

In an $A$.C. circuit the current

A
Always leads the voltage
B
Always lags behind the voltage
C
Is always in phase with the voltage
✓
May lead or lag behind or be in phase with the voltage

Answer

Correct option: D.

May lead or lag behind or be in phase with the voltage

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MCQ 1021 Mark

If the value of potential in an ac, circuit is $10 V$, then the peak value of potential is

A
$\frac{10}{\sqrt{2}}$
✓
$10 \sqrt{2}$
C
$20 \sqrt{2}$
D
$\frac{20}{\sqrt{2}}$

Answer

Correct option: B.

$10 \sqrt{2}$

(b) $V_0=\sqrt{2} V_{r m s}=10 \sqrt{2}$

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MCQ 1031 Mark

In a ac circuit of capacitance the current from potential is

✓
Forward
B
Backward
C
Both are in the same phase
D
None of these

Answer

Correct option: A.

Forward

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MCQ 1041 Mark

The phase difference between the current and voltage of LCR circuit in series combination at resonance is

✓
$0$
B
$\pi / 2$
C
$\pi$
D
$-\pi$

Answer

Correct option: A.

$0$

For purely $L$-circuit $P=0$

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MCQ 1051 Mark

For high frequency, a capacitor offers

A
More reactance
✓
Less reactance
C
Zero reactance
D
Infinite reactance

Answer

Correct option: B.

Less reactance

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MCQ 1061 Mark

The peak value of $220$ volts of ac mains is

A
$155.6$ volts
B
$220.0$ volts
✓
$311.0 $ volts
D
$440$ volts

Answer

Correct option: C.

$311.0 $ volts

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MCQ 1071 Mark

An inductive circuit contains a resistance of $10 \ ohm$ and an inductance of $2.0$ henry. If an ac voltage of $120$ volt and frequency of $60 \ Hz$ is applied to this circuit, the current in the circuit would be nearly

A
$0.32\ amp$
✓
$0.16 \ amp$
C
$048 \ amp$
D
$0.80 \ amp$

Answer

Correct option: B.

$0.16 \ amp$

$ Z=\sqrt{R^2+X_L^2}$
$=\sqrt{10^2+(2 \pi \times 60 \times 2)^2}=753.7 $
$ \therefore i=\frac{120}{753.7}=0.159 \mathrm{~A}$

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MCQ 1081 Mark

When $100$ volts dc is supplied across a solenoid, a current of $1.0$ amperes flows in it. When $100$ volts ac is applied across the same coil, the current drops to $0.5$ ampere. If the frequency of ac source is $50\ Hz$, then the impedance and inductance of the solenoid are

✓
$200 \Omega$ and $0.55$ henry
B
$100 \Omega$ and $0.86$ henry
C
$200 \Omega$ and $1.0$ henry
D
$100 \Omega$ and $0.93$ henry

Answer

Correct option: A.

$200 \Omega$ and $0.55$ henry

(a) For dc, $R=\frac{V}{i}=\frac{100}{1}=100 \Omega$
For ac, $Z=\frac{V}{i}=\frac{100}{0.5}=200 \Omega$
$\because Z=\sqrt{R^2+(\omega L)^2} \Rightarrow 200=\sqrt{(100)^2+4 \pi^2(50)^2 L^2} $
$ \therefore L=0.55\ H$

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MCQ 1091 Mark

In a $L C R$ circuit having $L=8.0$ henry, $C=0.5 \mu F$ and $R=100$ ohm in series. The resonance frequency in per second is

A
$600$ radian
B
$600 Hz$
✓
$500$ radian
D
$500\ Hz$

Answer

Correct option: C.

$500$ radian

(c) Resonance frequency in radian/second is
$\omega=\frac{1}{\sqrt{L C}}=\frac{1}{\sqrt{8 \times 0.5 \times 10^{-6}}}=500 \mathrm{rad} / \mathrm{sec}$

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MCQ 1101 Mark

In a circuit containing an inductance of zero resistance, the e.m.f. of the applied ac voltage leads the current by

✓
$90$
B
$ 45$
C
$30$
D
$0$

Answer

Correct option: A.

$90$

In a pure inductor (zero resistance), voltage leads the current by $90^{\circ}$ i.e. $\pi / 2$.

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MCQ 1111 Mark

An alternating voltage is connected in series with a resistance $R$ and an inductance $L$ If the potential drop across the resistance is $200\ V$ and across the inductance is $150\ V$, then the applied voltage is

A
$350\ V$
✓
$250\ V$
C
$500\ V$
D
$300 \ V$

Answer

Correct option: B.

$250\ V$

The applied voltage is given by $V=\sqrt{V_R^2+V_L^2}$
$v=\sqrt{(200)^2+(150)^2}=250 \text { volt }$

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MCQ 1121 Mark

The resistance of a coil for $dc$ is in ohms. In ac, the resistance

A
Will remain same
✓
Will increase
C
Will decrease
D
Will be zero

Answer

Correct option: B.

Will increase

The coil having inductance $L$ besides the resistance $R$. Hence for ac it's effective resistance $\sqrt{R^2+X_L^2}$ will be larger than it's resistance $R$ for dc.

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MCQ 1131 Mark

If a current $l$ given by $I_0 \sin \left(\omega t-\frac{\pi}{2}\right)$ flows in an ac circuit across which an ac potential of $E=E_0 \sin \omega t$ has been applied, then the power consumption $P$ in the circuit will be

A
$P=\frac{E_0 I_0}{\sqrt{2}}$
B
$P=\sqrt{2} E_0 I_0$
C
$P=\frac{E_0 I_0}{2}$
✓
$P=0$

Answer

Correct option: D.

$P=0$

Phase angle $\phi=90^{\circ}$, so power $P=V i \cos \phi=0$

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MCQ 1141 Mark

An ac source is connected to a resistive circuits. Which of the following is true

A
Current leads the voltage and both are in same phase
B
Current lags behind the voltage and both are in same phase
✓
Current and voltage are in same phase
D
Any of the above may be true depending upon the value of resistance

Answer

Correct option: C.

Current and voltage are in same phase

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MCQ 1151 Mark

The power is transmitted from a power house on high voltage ac because

A
Electric current travels faster at higher volts
✓
It is more economical due to less power wastage
C
It is difficult to generate power at low voltage
D
Chances of stealing transmission lines are minimized

Answer

Correct option: B.

It is more economical due to less power wastage

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MCQ 1161 Mark

Choke coil is used to control

✓
$ac$
B
$dc$
C
Both $ac$ and $dc$
D
Neither $ac$ nor $dc$

Answer

Correct option: A.

$ac$

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MCQ 1171 Mark

An alternating current of frequency ${ }^{\prime} f^{\prime}$ is flowing in a circuit containing a resistance $R$ and a choke $L$ in series. The impedance of this circuit is

A
$R+2 \pi f$
✓
$\sqrt{R^2+4 \pi^2 f^2 L^2}$
C
$\sqrt{R^2+L^2}$
D
$\sqrt{R^2+2 \pi f L}$

Answer

Correct option: B.

$\sqrt{R^2+4 \pi^2 f^2 L^2}$

$Z=\sqrt{R^2+X_L^2}, X_L=\omega L$ and $\omega=2 \pi f$
$\therefore Z=\sqrt{R^2+4 \pi^2 f^2 L^2}$

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MCQ 1181 Mark

The natural frequency of a $L-C$ circuit is equal to

A
$\frac{1}{2 \pi} \sqrt{L C}$
✓
$\frac{1}{2 \pi \sqrt{L C}}$
C
$\frac{1}{2 \pi} \sqrt{\frac{L}{C}}$
D
$\frac{1}{2 \pi} \sqrt{\frac{C}{L}}$

Answer

Correct option: B.

$\frac{1}{2 \pi \sqrt{L C}}$

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MCQ 1191 Mark

The potential difference $V$ and the current $i$ flowing through an instrument in an ac circuit of frequency $f$ are given by $V=5 \cos \omega t$ volts and $l=2 \sin \omega t$ amperes (where $\omega=2 \pi f)$. The power dissipated in the instrument is

✓
Zero
B
$10 W$
C
$5 W$
D
$2.5 W$

Answer

Correct option: A.

Zero

$V=5 \cos \omega t=5 \sin \left(\omega t+\frac{\pi}{2}\right)$ and $i=2 \sin \omega t$
Power $=V_{\text {r.m.s. }} \times i_{\text {r.m.s. }} \times \cos \phi=0$(Since $\phi=\frac{\pi}{2}$, therefore $\left.\cos \phi=\cos \frac{\pi}{2}=0\right)$

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MCQ 1201 Mark

The average power dissipated in a pure inductor of inductance $L$ when an ac current is passing through it, is(Inductance of the coil $L$ and current $I$ )

A
$\frac{1}{2} L I^2$
B
$\frac{1}{4} L I^2$
C
$2 Li ^2$
✓
Zero

Answer

Correct option: D.

Zero

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MCQ 1211 Mark

If $E_0$ represents the peak value of the voltage in an ac circuit, the r.m.s. value of the voltage will be

A
$\frac{E_0}{\pi}$
B
$\frac{E_0}{2}$
C
$\frac{E_0}{\sqrt{\pi}}$
✓
$\frac{E_0}{\sqrt{2}}$

Answer

Correct option: D.

$\frac{E_0}{\sqrt{2}}$

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MCQ 1221 Mark

In a circuit $L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^{\circ}$. The value of $C$ is

✓
$\frac{1}{2 \pi f(2 \pi f L+R)}$
B
$\frac{1}{\pi f(2 \pi f L+R)}$
C
$\frac{1}{2 \pi f(2 \pi f L-R)}$
D
$\frac{1}{\pi f(2 \pi f L-R)}$

Answer

Correct option: A.

$\frac{1}{2 \pi f(2 \pi f L+R)}$

$ \tan \phi=\frac{X_C-X_L}{R} \Rightarrow \tan 45^{\circ}=\frac{\frac{1}{2 \pi f C}-2 \pi f L}{R}$
$ \Rightarrow C=\frac{1}{2 \pi f(2 \pi f L+R)}$

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MCQ 1231 Mark

In an ac circuit with voltage $V$ and current $l$, the power dissipated is

A
$V I$
B
$\frac{1}{2} V I$
C
$\frac{1}{\sqrt{2}} V I$
✓
Depends on the phase between $V$ and $I$

Answer

Correct option: D.

Depends on the phase between $V$ and $I$

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MCQ 1241 Mark

In an ac circuit, the current is given by $i=5 \sin \left(100 t-\frac{\pi}{2}\right)$ and the ac potential is $V=200 \sin (100)$ volt. Then the power consumption is

A
$20$ watts
B
$40$ watts
C
$1000$ watts
✓
$0$ watt

Answer

Correct option: D.

$0$ watt

$P=V i \cos \phi$
Phase difference $\phi=\frac{\pi}{2} \Rightarrow P=z e r o$

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MCQ 1251 Mark

The current ' $i$ in an inductance coil varies with time ' $t$ ' according to following graph

Which one of the following plots shows the variations of voltage in the coil

Answer

Correct option: B.

(b) (1) For time interval $0

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MCQ 1261 Mark

In a region of uniform magnetic induction $B=10^{-2}$ tesla, a circular coil of radius $30 cm$ and resistance $\pi ohm$ is rotated about an axis which is perpendicular to the direction of $B$ and which forms a diameter of the coil. If the coil rotates at $200 rpm$ the amplitude of the alternating current induced in the coil is

A
$4 \pi m A$
B
$30 mA$
✓
$6 mA$
D
$200 mA$

Answer

Correct option: C.

$6 mA$

$ \text { Amplitude of } a c=i_0=\frac{V_0}{R}=\frac{\omega N B A}{R}=\frac{(2 \pi v) N B\left(\pi r^2\right)}{R} $
$ \Rightarrow i_0=\frac{2 \pi \times \frac{200}{60} \times 1 \times 10^{-2} \times \pi \times(0.3)^2}{\pi^2}=6 \mathrm{~mA}$

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MCQ 1271 Mark

An $L C R$ circuit contains $R=50 \Omega, L=1 mH$ and $C=0.1 \mu F$. The impedance of the circuit will be minimum for a frequency of

A
(a) $\frac{10^5}{2 \pi} s^{-1}$
B
(b) $\frac{10^6}{2 \pi} s^{-1}$
C
(c) $2 \pi \times 10^5 s^{-1}$
✓
(d) $2 \pi \times 10^6 s ^{-1}$

Answer

Correct option: D.

(d) $2 \pi \times 10^6 s ^{-1}$

(d) $i=\frac{220}{\sqrt{(20)^2+(2 \times \pi \times 50 \times 0.2)^2}}=\frac{220}{66}=3.33 \mathrm{~A}$

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MCQ 1281 Mark

The frequency of an alternating voltage is $50 cycles / sec$ and its amplitude is $120 V$. Then the r.m.s. value of voltage is

A
$101.3 V$
✓
$84.8 V$
C
$70.7 V$
D
$56.5 V$

Answer

Correct option: B.

$84.8 V$

$V_{r m s}=\frac{V_0}{\sqrt{2}}=\frac{120}{1.414}=84.8 \mathrm{~V}$

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MCQ 1291 Mark

If resistance of $100 \Omega$, inductance of $0.5$ henry and capacitance of $10 \times 10^{-6} F$ are connected in series through $50 Hz$ ac supply, then impedance is

A
$1.876$
B
$18.76$
✓
$189.72$
D
$101.3$

Answer

Correct option: C.

$189.72$

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MCQ 1301 Mark

The diagram shows a capacitor $C$ and a resistor $R$ connected in series to an ac source. $V_1$ and $V_2$ are voltmeters and $A$ is an ammeter

Consider now the following statements1. Readings in $A$ and $V$ are always in phase11. Reading in $V$ is ahead in phase with reading in $V$,111. Readings in $A$ and $V$ are always in phase which of these statements are/is correct

A
(a) 1 only
✓
(b) 11 only
C
(c) 1 and 11 only
D
(d) 11 and 111 only

Answer

Correct option: B.

(b) 11 only

(b) In $R C$ series circuit voltage across the capacitor leads the voltage across the resistance by $\frac{\pi}{2}$

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MCQ 1311 Mark

An ac supply gives $30\ V$ r.m.s. which passes through a $10 \Omega$ resistance. The power dissipated in it is

A
$90 \sqrt{2} W$
✓
$90 W$
C
$45 \sqrt{2} W$
D
$45 W$

Answer

Correct option: B.

$90 W$

$P=\frac{V_{m s}^2}{R}=\frac{(30)^2}{10}=90 \mathrm{~W}$

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MCQ 1321 Mark

The coil of choke in a circuit

A
Increases the current
✓
Decreases the current
C
Does not change the current
D
Has high resistance to dc circuit

Answer

Correct option: B.

Decreases the current

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MCQ 1331 Mark

Alternating current can not be measured by dc ammeter because

A
ac cannot pass through dc ammeter
✓
Average value of complete cycle is zero
C
ac is virtual
D
ac changes its direction

Answer

Correct option: B.

Average value of complete cycle is zero

In $d c$ ammeter, a coil is free to rotate in the magnetic field of a fixed magnet.If an alternating current is passed through such a coil, the torque will reverse it's direction each time the current changes direction and the average value of the torque will be zero.

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MCQ 1341 Mark

In an $L C R$ series ac circuit, the voltage across each of the components, $L, C$ and $R$ is $50 V$. the voltage across the $L C$ combination will be

A
$50 V$
B
$50 \sqrt{2} V$
C
$100 V$
✓
$0 V$ (zero)

Answer

Correct option: D.

$0 V$ (zero)

Net voltage across $L C$ combination $=V_L-V_C=0 \mathrm{~V}$

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MCQ 1351 Mark

In a $L C R$ circuit capacitance is changed from $C$ to $2 C$. For the resonant frequency to remain unchanged, the inductance should be change from $L$ to

A
$4 L$
B
$2 L$
✓
$L / 2$
D
$L / 4$

Answer

Correct option: C.

$L / 2$

$ v_0=\frac{1}{2 \pi \sqrt{L C}}$If $C$ changes to $2 C$ then for keeping $V$ constant $L$ must change to $L / 2$.

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MCQ 1361 Mark

An inductor of inductance $L$ and resistor of resistance $R$ are joined in series and connected by a source of frequency $\omega$. Power dissipated in the circuit is

A
$\frac{\left(R^2+\omega^2 L^2\right)}{V}$
✓
$\frac{V^2 R}{\left(R^2+\omega^2 L^2\right)}$
C
$\frac{V}{\left(R^2+\omega^2 L^2\right)}$
D
$\frac{\sqrt{R^2+\omega^2 L^2}}{V^2}$

Answer

Correct option: B.

$\frac{V^2 R}{\left(R^2+\omega^2 L^2\right)}$

$ P=V i \cos \phi=V\left(\frac{V}{Z}\right)\left(\frac{R}{Z}\right)=\frac{V^2 R}{Z^2}=\frac{V^2 R}{\left(R^2+\omega^2 L^2\right)}$

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MCQ 1371 Mark

The power factor of an ac circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $\omega$ is

✓
$R / \omega L$
B
$R /\left(R^2+\omega^2 L^2\right)^{1 / 2}$
C
$\omega L / R$
D
$R /\left(R^2-\omega^2 L^2\right)^{1 / 2}$

Answer

Correct option: A.

$R / \omega L$

$X_C=\frac{1}{2 \pi \nu C}$
$\Rightarrow C=\frac{1}{2 \pi \nu X_C}$
$=\frac{1}{2 \times \pi \times \frac{400}{\pi} \times 25}$
$=50 \mu F$

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MCQ 1381 Mark

Radio frequency choke uses core of

✓
Air
B
Iron
C
Air and iron
D
None of these

Answer

Correct option: A.

Air

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MCQ 1391 Mark

In an ac circuit, the r.m.s. value of current, $l$ is related to the peak current, $l$ by the relation

A
$I_{r m s}=\frac{1}{\pi} I_0$
✓
$I_{m s}=\frac{1}{\sqrt{2}} I_0$
C
$I_{r m s}=\sqrt{2} I_0$
D
$I_{r m s}=\pi I_0$

Answer

Correct option: B.

$I_{m s}=\frac{1}{\sqrt{2}} I_0$

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MCQ 1401 Mark

The quality factor of $\text{LCR}$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by

✓
$\frac{\omega L}{R}$
B
$\frac{R}{\omega L}$
C
$\left(\frac{\omega L}{R}\right)^{1 / 2}$
D
$\left(\frac{\omega L}{R}\right)^2$

Answer

Correct option: A.

$\frac{\omega L}{R}$

$i=\frac{V}{X_L}=\frac{200}{\omega L}=\frac{200}{2 \pi \times 50 \times 1}=0.637 \mathrm{~A}$

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MCQ 1411 Mark

The value of the current through an inductance of $1H$ and of negligible resistance, when connected through an ac source of $200 V$ and $50 Hz$, is

✓
$0.637 A$
B
$1.637 A$
C
$2.637 A$
D
$3.637 A$

Answer

Correct option: A.

$0.637 A$

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MCQ 1421 Mark

In an ac circuit, the potential difference across an inductance and resistance joined in series are respectively $16 V$ and $20 V$. The total potential difference across the circuit is

A
$20.0 V$
✓
$25.6 V$
C
$31.9 V$
D
$53.5 V$

Answer

Correct option: B.

$25.6 V$

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MCQ 1431 Mark

An electric lamp is connected to $220 V, 50 Hz$ supply. Then the peak value of voltage is

A
$210 V$
B
$211 V$
✓
$311 V$
D
$320 V$

Answer

Correct option: C.

$311 V$

$V_0=V_{r m s} \times \sqrt{2}=220 \times \sqrt{2}=311$

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MCQ 1441 Mark

The $i$ - $v$ curve for anti-resonant circuit is

Answer

Correct option: B.

(b) For anti-resonant circuit current is minimum at resonant frequency and at frequencies other than resonant frequency current rises with frequency.

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MCQ 1451 Mark

The resonance point in $X_L-f$ and $X_C-f$ curves is

A
(a) $P$
B
(b) $Q$
✓
(c) $R$
D
(d) $S$

Answer

Correct option: C.

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MCQ 1461 Mark

The vector diagram of current and voltage for a circuit is as shown. The components of the circuit will be

A
$L C R$
B
$L R$
✓
$L C R$ or $L R$
D
None of these $i_{r m s}=25 amp$

Answer

Correct option: C.

$L C R$ or $L R$

From phasor diagram it is clear that current is lagging with respect to $E$.
This may be happen in $L C R$ or $L R$ circuit.

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MCQ 1471 Mark

In pure inductive circuit, the curves between frequency $f$ and reciprocal of inductive reactance $1 / X$ is

Answer

Correct option: C.

$X_L=2 \pi f L \Rightarrow X_L \propto f \Rightarrow \frac{1}{X_L} \propto \frac{1}{f}$
i.e., graph between $\frac{1}{X_L}$ and $f$ will be a hyperbola.

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MCQ 1481 Mark

Two sinusoidal voltages of the same frequency are shown in the diagram. What is the frequency, and the phase relationship between the voltages

Frequency in $Hz$ Phase lead of $N$ over $M$ in radians(a) 0.4$-\pi / 4$$-\pi / 2$$+\pi / 2$$-\pi / 4$

A
$0.4$
✓
$2.5$
C
$3.5$
D
$5.3$

Answer

Correct option: B.

$2.5$

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MCQ 1491 Mark

The output current versus time curve of a rectifier is shown in the figure. The average value of output current in this case is

A
$0$
B
$\frac{I_0}{2}$
✓
$\frac{2 I_0}{\pi}$
D
$I_0$

Answer

Correct option: C.

$\frac{2 I_0}{\pi}$

$I_{a v}=\frac{\int_0^{T / 2} i d t}{\int_0^{T / 2} d t}=\frac{\int_0^{T / 2} I_0 \sin (\omega t) d t}{T / 2}$
$ =\frac{2 I_0}{T}\left[\frac{-\cos \omega t}{\omega}\right]_0^{T / 2}=\frac{2 I_0}{T}\left[-\frac{\cos \left(\frac{\omega T}{2}\right)}{\omega}+\frac{\cos 0^{\circ}}{\omega}\right] $
$ =\frac{2 I_0}{\omega T}\left[-\cos \pi+\cos 0^{\circ}\right]=\frac{2 I_0}{2 \pi}[1+1]=\frac{2 I_0}{\pi}$

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MCQ 1501 Mark

A constant voltage at different frequencies is applied across a capacitance $C$ as shown in the figure. Which of the following graphs
Correctly depicts the variation of current with frequency?

Answer

Correct option: B.

For capacitive circuits $X_C=\frac{1}{\omega C}$$\therefore i=\frac{V}{X_C}=V \omega C \Rightarrow i \propto \omega$

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JEE physics MCQ