Video Lecture
Theory For Making Notes
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Practice Questions (Basic Level)
Q.1
An L–C–R series circuit is connected to a source of alternating current. At resonance the applied voltage and current flowing through the circuit will have a phase difference of
(a) zero (b) π / 4 (c) π / 2 (d) π
Ans. (a)
Q.2
In a series L–C–R circuit the voltage across resistance, capacitance and inductance is 10 V each. If the capacitance is short circuited, the voltage across the inductance will be
(a) \displaystyle \frac{{10}}{{\sqrt{2}}}\,V
(b) 10 V
(c) \displaystyle 10\sqrt{2}\,V
(d) 20 V
Ans. (a)
Q.3
In the given figure, a series L–C–R circuit is connected to a variable frequency source of 230V. The impedance and amplitude of the current at the resonating frequency will be
(a) 20 Ω and 4.2 A
(b) 30 Ω and 6.9 A
(c) 25 Ω and 5.8 A
(d) 40 Ω and 5.75 A
Ans. (d)
Q.4
In the series L–C–R circuit shown, the impedance is
(a) 200 Ω
(b) 100 Ω
(c) 300 Ω
(d) 500 Ω
Ans. (d)
Q.5
The power factor of an R–L circuit is \displaystyle \frac{1}{{\sqrt{2}}}. If the frequency of AC is doubled, what will be the power factor ?
(a) \displaystyle \frac{1}{{\sqrt{3}}}
(b) \displaystyle \frac{1}{{\sqrt{5}}}
(c) \displaystyle \frac{1}{{\sqrt{7}}}
(d) \displaystyle \frac{1}{{\sqrt{{11}}}}
Ans. (b)
Q.6
In the circuit shown in figure neglecting source resistance, the voltmeter and ammeter readings will be respectively
(a) 0 V, 3 A (b) 150 V, 3 A (c) 150 V, 6 A (d) 0 V, 8 A
Ans. (d)
Q.7
The impedance of a circuit, when a resistance R and an inductor of inductance L are connected in series in an AC circuit of frequency f, is
(a) \displaystyle \sqrt{{R+2{{\pi }^{2}}{{f}^{2}}{{L}^{2}}}}
(b) \displaystyle \sqrt{{R+4{{\pi }^{2}}{{f}^{2}}{{L}^{2}}}}
(c) \displaystyle \sqrt{{{{R}^{2}}+4{{\pi }^{2}}{{f}^{2}}{{L}^{2}}}}
(d) \displaystyle \sqrt{{{{R}^{2}}+2{{\pi }^{2}}{{f}^{2}}{{L}^{2}}}}
Ans. (c)
Q.8
Voltage and current in an AC circuit are given by \displaystyle V=5\sin \left( {100\,\pi t-\frac{\pi }{6}} \right) and \displaystyle I=4\sin \left( {100\,\pi t+\frac{\pi }{6}} \right).
(a) voltage leads the current by 30º
(b) current leads the voltage by 30º
(c) current leads the voltage by 60º
(d) voltage leads the current by 60º
Ans. (c)
Q.9
An inductance of 1 mH, a condenser of 10 µF and a resistance of 50 Ω are connected in series. The reactances of inductor and condensers are same. The reactance of either of them will be
(a) 100 Ω (b) 30 Ω (c) 3.2 Ω (d) 10 Ω
Ans. (d)
Q.10
In L–C–R circuit, the capacitance is changed from C to 4C. For the same resonant frequency, the inductance should changed from L to
(a) 2 L (b) L / 2 (c) L / 4 (d) 4 L
Ans. (c)
Q.11
The resonant frequency of a circuit is f. If the capacitance is made 4 times the initial value, then the resonant frequency will become
(a) f / 2 (b) 2 f (c) f (d) f / 4
Ans. (a)
12.
In a series R-L-C circuit, R = 100 \displaystyle \Omega , XL = 300 \displaystyle \Omega and Xc = 200 \displaystyle \Omega . The phase angle \displaystyle \phi of the circuit is
(A) 00
(B) 900
(C) 450
(D) – 450
Ans (C)
13.
In a series LRC circuit, resonance occurs when
(A) R = XL ~ XC
(B) XL = XC
(C) XL = 10 XC more
(D) XL – XC> R
Ans (B)
14.
The power factor in AC circuit is equal to
(A) Z/R
(B) R/Z
(C) RZ
(D) none of the above
Ans (B)
15.
A series AC circuit has a resistance of 12 \displaystyle \Omega and reactance 5 \displaystyle \Omega . The impedance of circuit is
(A) 5 \displaystyle \Omega
(B) 12 \displaystyle \Omega
(C) 13 \displaystyle \Omega
(D) 17 \displaystyle \Omega
Ans (C)
16.
By what percentage the reactance in an AC circuit should be increased so that the power factor changes from (1/2) to (1/4)?
(a) 200%
(b) 100%
(c) 50%
(d) 400%
Ans (b)
17.
The angular frequency of a resonant LC combination (L = 10mH and C = 1 \displaystyle \mu F) is
(a) 1.0 × 104 radian per sec
(b) 1.0 × 104 Hz
(c) 1.0 × 10–4 radian per sec
(d) 1.0 × 10–4 Hz
Ans (a)
18.
An inductance coil of 1 Henry and a condenser of capacity 1pF produce resonance. The resonant frequency will be
(a) \frac{{{{{10}}^{6}}}}{{2\pi }}Hz
(b) \frac{{{{{10}}^{6}}}}{\pi }Hz
(c) \frac{{2\pi }}{{{{{10}}^{6}}}}Hz
(d) 2 \displaystyle \pi ´ 106 Hz
Ans (a)
Practice Questions (JEE Main Level)
Q.1
In a series LCR circuit, the frequencies f1 and f2 at which the current amplitude falls to \frac{1}{{\sqrt{2}}} of the current at resonance, are separated by an interval equal to (R/2pL).
(a) \displaystyle \frac{{2R}}{{\pi L}}
(b) \displaystyle \frac{R}{{2\pi L}}
(c) \displaystyle \frac{{7R}}{{2\pi L}}
(d) \displaystyle \frac{R}{L}
Ans : (b)
Q.2
A circuit element is placed in a black box. At t = 0, switch is closed and the current flowing through the circuit element and the voltage across its terminals are recorded to have the wave shapes shown in the figure. The type of element and its magnitude are
(a) inductance of 4 H
(b) resistance of 4 W
(c) capacitance of 1 F
(d) a voltage source of emf 4 V
Ans. (c)
Q.3
The adjoining figure shows on A.C. circuit with resistance R, inductance L and source voltage Vs.
4.
In an a.c. circuit voltage v and current i are given by v = 100 sin 100 t volts,
i = 100 sin {100 t + \displaystyle \pi /3} mA. The power dissipated in the circuit is
(A) 104 W
(B) 10 W
(C) 2.5 W
(D) 5 W
Ans (D)
5.
In the a.c. circuit shown in the following figure, the resultant potential difference is
(A) 110 V
(B) 10 V
(C) 50 V
(D) 70 V
Ans (C)
6.
An alternating voltage E = E0 sin \displaystyle \omega t, is applied across a coil of inductor L. The current flowing through the circuit at any instant t is
(A) E0 / \displaystyle \omega L sin ( \displaystyle \omega t + \displaystyle \pi /2)
(B) E0 / \displaystyle \omega L sin ( \displaystyle \omega t – \displaystyle \pi /2)
(C) E0 \displaystyle \omega L sin ( \displaystyle \omega t – \displaystyle \pi /2)
(D) E0 \displaystyle \omega L sin ( \displaystyle \omega t + \displaystyle \pi /2)
Ans (B)
7.
In an R-L-C circuit v = 20 sin (314 t + 5 \displaystyle \pi /6) and i = 10 sin (314 t + 2 \displaystyle \pi /3) The power factor of the circuit is
(A) 0.5
(B) 0.966
(C) 0.866
(D) 1
Ans (C)
8.
The impedance of the circuit is
(A) \sqrt{{{{R}^{2}}+{{{\left( {\frac{{\omega L}}{{1-{{\omega }^{2}}LC}}} \right)}}^{2}}}}
(B) \sqrt{{\frac{1}{{{{R}^{2}}}}+{{{\left( {\frac{1}{{\omega L-1/\omega C}}} \right)}}^{2}}}}
(C) \sqrt{{{{R}^{2}}+{{{\left( {\omega L-\frac{1}{{1-\omega C}}} \right)}}^{2}}}}
(D) none of the above
Ans (A)
9.
In a series LCR circuit, the frequencies {{f}_{1}} and {{f}_{2}} at which the current amplitude falls to 1/\sqrt{2} of the current amplitude at resonance are separated by frequency interval
(a) \frac{R}{{2\pi L}}
(b) 2\pi \sqrt{{LC}}
(c) \sqrt{{LC}}
(d) RC
Ans (a)
10.
An alternating potential V={{V}_{0}}\sin \omega t is applied across a circuit. As a result, the current I={{I}_{0}}\sin \left( {\omega t-\frac{\pi }{2}} \right) flows in it. The power consumed in the circuit per cycle is
(a) zero
(b) 0.5 {{V}_{0}}{{I}_{0}}
(c) 0.707 {{V}_{0}}{{I}_{0}}
(d) 1.414 {{V}_{0}}{{I}_{0}}
Ans (a)
11.
What is the r.m.s. value of an alternating current which when passed through a resistor produce heat which is thrice that produced by a current of 2 ampere in the same resistor
(a)6.00A
(b) 2.00 A
(c)3.46A
(d) 0.65 A
Ans (c)
12.
An alternating voltage V = V0 sin \displaystyle \omega t is connected to a capacitor of capacity C0 through an AC ammeter of zero resistance. The reading of ammeter is
(a) \frac{{{{V}_{0}}\sqrt{2}}}{{\omega C}}
(b) \frac{{{{V}_{0}}}}{{\omega C\sqrt{2}}}
(c) \frac{{{{V}_{0}}\omega C}}{{\sqrt{2}}}
(d) none of these
Ans (c)
13.
Calculate the r.m.s. value of e.m.f. given by E=50\sqrt{2}\sin \left( {\omega t-\frac{\pi }{4}} \right)
(a) 50 V
(b) 5 V
(c) 2\sqrt{5}V
(d) None of these
Ans (a)
14.
An inductance coil of 1 Henry and a condenser of capacity 1pF produce resonance. The resonant frequency will be
(a) \frac{{{{{10}}^{6}}}}{{2\pi }}Hz
(b) \frac{{{{{10}}^{6}}}}{\pi }Hz
(c) \frac{{2\pi }}{{{{{10}}^{6}}}}Hz
(d) 2 \displaystyle \pi ´ 106 Hz
Ans (a)
15.
An alternating voltage V = V0 sin wt is applied across a circuit. As a result a current I = I0 sin ( \displaystyle \omega t – \displaystyle \pi /2) flows in it. The power consumed per cycle is
(a) zero
(b) 0.5 V0I0
(c) 0.707 V0I0
(d)1.414 V0I0
Ans (a)
16.
Using an AC voltmeter the potential difference in the electrical line in a house is read to be
234 volt. If the line frequency is known to be 50 cycles/second, the equation for the line voltage is
(a) V = 165 sin (100 pt)
(b) V = 331 sin (100 pt)
(c) V = 220 sin (100 pt)
(d) V = 440 sin (100 pt)
Ans (b)
Practice Questions (JEE Advance Level)
1.
In an L–R circuit, the inductive reactance is equal to the resistance R of the circuit. An emf
E = E0 cos ( \displaystyle \omega t) is applied to the circuit. The power consumed in the circuit is
(a) \frac{{E_{0}^{2}}}{{\sqrt{2}R}}
(b) \frac{{E_{0}^{2}}}{{4R}}
(c) \frac{{E_{0}^{2}}}{{2R}}
(d) \frac{{E_{0}^{2}}}{{8R}}
Ans (b)
2.
In the series LCR circuit, the voltmeter and ammeter readings are respectively
(a) V = 100 V, I = 2 A
(b) V = 1000 V, I = 5 A
(c) V = 1000 V, I = 2 A
(d) V = 300 V, I = 1 A
Ans (a)
3.
The current flowing through the resistor in a series L–C–R a.c. circuit, is I=\varepsilon /R.. Now the inductor and capacitor are connected in parallel and joined in series with the resistor as shown in figure. The current in the circuit is now. (Symbols have their usual meaning)
(a) equal to I
(b) more than I
(c) less than I
(d)zero
Ans (d)
4.
In a RLC series circuit shown, the readings of voltmeters and are 100 V and 120 V, respectively. If source voltage is 130 V
(a) Voltage across resistor is 50 V.
(b) Voltage across inductor is 86.6 V.
(c) Voltage across Capacitor is 206.6 V
(d) All of these
Ans (d)
5.
In the circuit shown in figure, the a.c. source gives a voltage V = 12cos(2000t). Neglecting source resistance, the current in the circuit will be
(a) 0 A
(b) 2 A
(c) 1.4 A
(d) 0.5 A
Ans (c)
6.
The power factor of wattless current is
(a) 0
(b) 1/2
(c) 1
(d) \displaystyle \infty
Ans (a)
7.
In the circuit shown in the figure, if both the bulbs B1 and B2 are identical, then
(a) their brightness will be the same
(b) as frequency of supply voltage is increased, brightness of B1 will decrease and that of B2 will increase
(c) as frequency of supply voltage is increased, brightness of B1 will increase and that of B2 will decrease
(d) only B2 will glow because the capacitor has infinite impedance.
Ans (c)
8.
A 750 Hz, 20 volt source is connected to a resistance of 100 ohm, an inductance of \frac{1}{{1000\pi }}H and a capacitance of \frac{1}{{2250\pi }}F, all in series. The time in which the temperature of the resistance increases by 10°C is (thermal capacity = 2 SI unit) (a) 2.5 sec
(b) 5 sec
(c) 7. 5sec
(d) 10 sec
Ans (b)
9.
A capacitor and resistor are connected with an A.C. source as shown in figure. Reactance of capacitor is XC= 3 \displaystyle \Omega and resistance of resistor is 4\Omega . Phase difference between current I and I1 is \left[ {{{{\tan }}^{{-1}}}\left( {\frac{4}{3}} \right)=53{}^\text{o}} \right]
(a)900
(b)zero
(c)53º
(d) 37º
Ans (c)
10.
A circuit consists of a capacitor and a resistor having resistance R = 220 \displaystyle \Omega connected in series. When an alternating e.m.f. of peak voltage V0 = 220 \sqrt{2} V is applied to the circuit, the peak current in steady state is observed to be I0 = 1A. The phase difference between the current and the voltage is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Ans (b)
Comprehension ( Question No.- 11 to 14 )
One application of LRC series circuits is to high pass or low pass filters, which filter out either the low or high frequency components of a signal. A high pass filter is shown in figure, where the output voltage is taken across the LR combination, where LR combination represents an inductance coil that also has resistance due to large length of the wire in the coil.
11.
The ratio of Vout/Vs as a function of the angular frequency \displaystyle \omega of the source is
(a) \sqrt{{\frac{{{{R}^{2}}+\omega {{L}^{2}}}}{{{{R}^{2}}+{{{\left( {\omega L-\frac{1}{{\omega C}}} \right)}}^{2}}}}}}
(b) \sqrt{{\frac{{{{R}^{2}}+{{{\left( {\omega L} \right)}}^{2}}}}{{{{R}^{2}}+{{{\left( {\omega L-\frac{1}{{\omega C}}} \right)}}^{2}}}}}}
(c) \sqrt{{\frac{{{{R}^{2}}+{{\omega }^{2}}L}}{{{{R}^{2}}+{{{\left( {\omega C-\frac{1}{{\omega L}}} \right)}}^{2}}}}}}
(d) 1
Ans (b)
12.
If \displaystyle \omega is negligibly small then the value of Vout /Vs is
(a) \displaystyle \omega RC
(b) \frac{{\omega R}}{L}
(c) \frac{{\omega R}}{L}RL
(d) \frac{{\omega R}}{C}
Ans (a)
13.
For large value of \frac{{\omega R}}{C}, the value of Vout/Vs is
(a) 1
(b) \frac{{\omega R}}{C}RC
(c) \frac{{\omega R}}{C}RL
(d) \frac{{\omega R}}{L}
Ans (a)
14.
The ratio of Vout/Vs at resonance is
(a) \sqrt{{\frac{{{{R}^{2}}+{{{\left( {\omega L} \right)}}^{2}}}}{{{{{\left( {\omega L} \right)}}^{2}}}}}}
(b) \sqrt{{\frac{{{{R}^{2}}+{{{\left( {\omega L} \right)}}^{2}}}}{{{{R}^{2}}}}}}
(c) \sqrt{{\frac{{{{R}^{2}}-\omega {{L}^{2}}}}{{{{R}^{2}}}}}}
(d) 1
Ans (b)
Comprehension ( Question No.- 15 to 17 )
Figure shows a basic AC bridge. The four arms of the bridge have impedances Z1, Z2, Z3 and Z4. The condition for balance of bridge require that there should be no current through the detector D. Basic equation for balance of AC bridge is {{Z}_{1}}{{Z}_{4}}={{Z}_{2}}{{Z}_{3}}. If we work in terms of rectangular co-ordinates then \left( {{{R}_{1}}+j{{X}_{1}}} \right)\left( {{{R}_{4}}+j{{X}_{4}}} \right)=\left( {{{R}_{2}}+j{{X}_{2}}} \right)\left( {{{R}_{3}}+j{{X}_{3}}} \right). Impedance (Z) for resistance is R,for inductor is jwL and for capacitor is \frac{1}{{j\omega C}}=-\frac{j}{{\omega C}}. Equivalent impedance in series is given by Z={{Z}_{1}}+{{Z}_{2}}+ ………….. and in parallel it is given by \frac{1}{Z}=\frac{1}{{{{Z}_{1}}}}+\frac{1}{{{{Z}_{2}}}}+……..
A complex equation is satisfied only if real and imaginary parts of each side of the equation are separately equal. Thus there are two independent conditions for both of them that must be satisfied for the bridge to be balanced.
15.
Value of Z2 is
(a) {{R}_{2}}+\frac{j}{{\omega {{C}_{2}}}}
(b) {{R}_{2}}+j\omega {{C}_{2}}
(c) {{R}_{2}}+\frac{1}{{j\omega {{C}_{2}}}}
(d) {{R}_{2}}+\frac{{{{C}_{2}}}}{{j\omega }}
Ans (c)
16.
Balance condition for real term is
(a) {{R}_{2}}{{R}_{3}}={{C}_{4}}{{L}_{1}}
(b) {{L}_{1}}={{R}_{2}}{{R}_{3}}{{C}_{4}}
(c) {{L}_{1}}{{C}_{2}}={{R}_{2}}{{R}_{3}}
(d) {{L}_{1}}{{R}_{2}}={{R}_{3}}{{C}_{4}}
Ans (b)
17.
If {{L}_{1}}={{R}_{2}}{{R}_{3}}\,\,{{C}_{4}} and there is no current in detector then \frac{{{{R}_{1}}}}{{{{R}_{3}}}} is
(a) \frac{{{{C}_{4}}}}{{{{C}_{2}}}}
(b) \frac{{{{C}_{2}}}}{{{{C}_{4}}}}
(c) {{C}_{4}}{{C}_{2}}
(d) \frac{1}{{{{C}_{2}}{{C}_{4}}}}
Ans (a)