Phasor Diagrams in AC Circuits

Q. In the following circuit, the current through the resistor $R(=2\Omega )$ is $I$ Amperes. The value of $I$ is

Q. The series of two batteries, both of the same emf $10\text{V}$, but different internal resitance of $20\Omega$ and $5\Omega$, is connected to the parallel combination of two resistors $30\Omega$ and $R\Omega$. The voltage difference across the battery of internal resistance $20\Omega$ is zero, the value of $R$ (in $\Omega$) is

Q. A current of 2A flows through a 2 ohm resistir when connected across a battery .The same battery supplies a current of 0.5A when connected across a 9ohm resistor. the internal resis†an ce of the battery is

Q.

The current in a conductor varies with time t as $I=3t+4t^2$, where I is in amperes and t in seconds. The electric charge that flows through the section of the conductor between t = 1 s and t = 3 s is

1. $\frac{140}{3}C$

2. $\frac{14}{3}C$

3. $\frac{3}{14}C$

4. $\frac{3}{140}C$

Q. What is a RC, LR, LC and LCR circuits ?

Q. The current in the branch CD of the circuit (in ampere) is

Q. A circuit contains two inductors of self-inductance $L_1$ and $L_2$ in series. If $M$ is the mutual inductance, then the effective inductance of the circuit shown will be

1. $L_1+L_2$
2. $L_1+L_2-2M$
3. $L_1+L_2+M$
4. $L_1+L_2+2M$

Q. If three waves, $y_1=A\sin (kx-\omega t),y_2=A\sin (kx-\omega t+\varphi )$ and $y_3=A\sin (kx-\omega t+2\varphi )$ are superimposed so that $y_1+y_2+y_3=0$ at al positions. Then the value of $\varphi$ will be

1. $-\frac{2\pi }{3}$
2. All of these
3. $\frac{4\pi }{3}$
4. $\frac{2\pi }{3}$

Q. As shown in figure two identical capacitors are connected to a battery of $V\text{volts}$ in parallel. When capacitors are fully charged, their stored energy is $U_1$. If the key $K$ is opened and material of dielectric constant ${\epsilon }_r=3$ is inserted in each capacitors their stored energy is now $U_2$. Then $\frac{U_1}{U_2}$ will be:

1. $\frac{3}{5}$
2. $\frac{5}{3}$
3. $\frac{4}{5}$
4. $\frac{5}{4}$

Q. If istantaneous value of current is 3+4sin(wt) Find the rms value

Q. In a pure inductive circuit or In an ac circuit containing inductance only, the current

1. Leads the e.m.f. by ${90}^{\circ }$
2. Lags behind the e.m.f. by ${90}^{\circ }$
3. Sometimes leads and sometime lags behind the e.m.f.
4. Is in phase with the e.m.f.

Q. A resistor and an inductor are connected in series across a voltage, $V=283\sin \left(314t\right)$. The current is found to be $4\sin (314t-\pi /4)$. The value of resistance of resistor is -

1. $10\Omega$
2. $30\Omega$
3. $50\Omega$
4. $70\Omega$

Q. The figure below shows a source of alternating voltage connected to a capacitor and a resistor. Which of the following phasor diagrams correctly describe the phase relationship between $I_c$ (current between the source and the capacitor) and $I_R$ (the current in the resistor)?

1. 
2. 
3. 
4. 

Q. 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 statements

1) Readings in A and $V_2$ are always in phase
2) Reading in $V_1$ is ahead in phase with reading in $V_2$
3) Readings in A and $V_1$ are always in phase which of these statements are / is correct

1. II only
2. I only
3. I and II only
4. II and III only

Q. In a black box of unknown elements ($L$ or $R$ or any other combination), an ac voltage $E=E_0\sin (\omega t+\varphi )$ is applied and current in the circuit was found to be $I=I_0\sin [\omega t+\varphi +\left(\frac{\pi }{4}\right)]$. Then the unknown elements in the box may be

1. Only capacitor
2. Inductor and resistor both
3. Only resistor
4. Either capacitor, resistor and inductor or only capacitor and resistor

Q. The variation of the instantaneous current (I) and the instantaneous emf (E) in a circuit is as shown in fig. Which of the following statements is correct

1. The voltage lags behind the current by π/2
2. The voltage leads the current by π/2
3. The voltage leads the current by π
4. The voltage and the current are in phase

Q. An amplitude modulated signal is plotted below which one of the following best describes the above signal ?

Q. For an $\text{LCR}$ series $\text{AC}$ circuit match the following two columns.
Column-1 Column-2

$\text{(a)}$ If resistance is increased.	$\text{(p)}$ current will increase.
$\text{(b)}$ If capacitance is increased.	$\text{(q)}$ current will decrease.
$\text{(c)}$ If inductance is increased.	$\text{(r)}$ current may increase or decrease.
$\text{(d)}$ If frequency is increased.	$\text{(s)}$ power may increase or decrease.

1. $\text{(a)}\to \text{(q, s)};\text{(b)}\to \text{(r, s)};\text{(c)}\to \text{(r, s)};\text{(d)}\to \text{(r, s)}$
2. $\text{(a)}\to \text{(p, s)};\text{(b)}\to \text{(r, s)};\text{(c)}\to \text{(r, s)};\text{(d)}\to \text{(p, s)}$
3. $\text{(a)}\to \text{(p, r)};\text{(b)}\to \text{(p, s)};\text{(c)}\to \text{(r, s)};\text{(d)}\to \text{(r, s)}$
4. $\text{(a)}\to \text{(p, s)};\text{(b)}\to \text{(p, s)};\text{(c)}\to \text{(q, s)};\text{(d)}\to \text{(r, s)}$

Q. A capacitor, of capacity $C$, is fully charged with voltage $V_0$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $\frac{C}{2}$. The energy loss in the process, after the charge is distributed between the two capacitors, is :

1. $\frac{1}{2}C{V}_0^2$
2. $\frac{1}{3}C{V}_0^2$
3. $\frac{1}{4}C{V}_0^2$
4. $\frac{1}{6}C{V}_0^2$

Q. The current passing through the battery immediately after key $\left(K\right)$ is closed (Initially all the capacitors are uncharged and the value of $R=6\Omega$ and $C=4\mu \text{F}$) is

1. $2\text{A}$
2. $4\text{A}$
3. $3\text{A}$
4. $1\text{A}$

Q. An alternating emf is applied across a parallel combination of a resistance $R$, capacitance $C$ and an inductance $L$. If $I_R,I_L,I_C$ are the currents through $R,L$ and $C$ respectively, then the diagram which correctly represents, the phase relationship among $I_R,I_L,I_C$ and source emf $E$, is given by

1. 
2. 
3. 
4. 

Q. What is the phase difference between $I$ and $E$ if $E=E_0\sin \left(\omega t\right)$ and $I=I_0\cos (\omega t+\frac{\pi }{3})$?

1. $\frac{\pi }{3}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{2}$
4. $\frac{5\pi }{6}$

Q. An inductor of inductance $L,$ a capacitor of capacitance $C$ and a resistor of resistance $R$ are connected in series to an ac source of potential difference $V\text{volt}$ as shown in figure. Potential difference across $L,C$ and $R$ is $40\text{V},10\text{V}$ and $40\text{V},$ respectively. The amplitude of current flowing through $LCR$ series circuit is $10\sqrt{2}\text{A}.$ The impedance of the circuit is

1. $5\Omega$
2. $4\sqrt{2}\Omega$
3. $5\sqrt{2}\Omega$
4. $4\Omega$

Q. A cyclotron is used to obtain 2MeV protons.if the frequency is 5MHz & potential is 20kV.the magnetic field necessary for resonance is

Q. A potential difference is applied to the plate of a capacitor filled with an insulator, with energy stored in the capacitor as U. The capacitor is disconnected and the insulator is pulled out now. The work done in pulling out the insulator against electric field is 4U. Find the dielectric constant of the insulator. ___

Q. in LC circuit , find time when energy store is completely electrical

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

1. $\text{LC}$
2. $\text{CR}$
3. $\text{LCR}$ (or) $\text{LR}$
4. None of these

Q. A series LCR circuit with $100\Omega$ resistance is connected to an AC source of $200\text{V}$ and angular frequency $300\text{rad/s}$. When only the capacitance is removed, the current lags behind the voltage by ${60}^{\circ }$. When only the inductance is removed, the current leads the voltage by ${60}^{\circ }$. The average power dissipated(in $\text{watt}$) in the LCR circuit is

Q.

A 5V battery with internal resistance 2Ω and a 2V battery with internal resistance 1Ω are connected in parallel with unlike polarities connected together. This combination is connected to 10Ω resistor, . The Current in the 10Ω resistor is

1) 0.27A

2) 0.05A

3) 0.25A

4) 0.3A

Q. A capacitor of capcitance $C$ has charge $Q$. It is connected to an identical capacitor through a resistance. The heat produced in the resistance is

1. $\frac{Q^2}{2C}$
   
2. $\frac{Q^2}{4C}$
   
3. $\frac{Q^2}{8C}$
   
4. Depends on the value of the resistance