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The current I, potential difference V_L across the inductor and potential difference V_C across the capacitor in the circuit as shown in the figure are best represented vectorially as:
                     
1.                                     2.
3.                                 4.

In the circuit shown, A is joined to B for a long, and then, A is joined to C. The total heat produced in R is:
                       
1.  $\frac{{\mathrm{L\epsilon }}^2}{{\mathrm{R}}^2}$
2.  $\frac{{\mathrm{L\epsilon }}^2}{2{\mathrm{R}}^2}$
3.  $\frac{{\mathrm{L\epsilon }}^2}{4{\mathrm{R}}^2}$
4.  $\frac{{\mathrm{L\epsilon }}^2}{8{\mathrm{R}}^2}$

A capacitor C=2$\mathrm{\mu }$F and an inductor with L=10 H and coil resistance 5$\mathrm{\Omega }$ are in series in a circuit. When an alternating current of r.m.s. value 2A flows in the circuit, the average power in watts in the circuit is:
1.  100
2.  50
3.  20
4.  10

A pure inductor L, a capacitor C and resistance R are connected across a battery of e.m.f. $\mathrm{\epsilon }$ and internal resistance r as shown in the figure. The switch ${\mathrm{S}}_{\mathrm{w}}$ is closed at t=0, select the correct alternative (s).
                               
1.  current through resistance R is zero all the time
2.  current through resistance R is zero at t=0 and t$\to \infty$
3.  maximum charge stored in the capacitor is CE
4.  maximum energy stored in the inductor is equal to the maximum energy stored in the capacitor

The current passing through the battery immediately after key (K) is closed [it is given that initially all the capacitors are uncharged (given that R=6$\mathrm{\Omega }$ and C=4$\mathrm{\mu }$F)] is:
                       
1.  1 A
2.  5 A
3.  3 A
4.  2 A

Select the correct circuit-diagram for a phasor diagram as shown in the adjacent Fig.
                                 
1.                        2.
3.                        4.

In the circuit shown, switch k₂ is closed at t=0. At time t=t₀, switch k₁ is opened and switch k₂ is simultaneously closed. The variation of inductor current with time is:
                           
1.                        2.
3.                     4.

In an A.C. sub-circuit (see in figure), the resistance R=0.2$\mathrm{\Omega }$. At a certain instant V_A-V_B=0.5V, I=0.5A, $\frac{△\mathrm{l}}{△\mathrm{t}}=8\mathrm{A}/\mathrm{s}.$ The inductance of the coil is:
                         
1.  0.01 H
2.  0.02 H
3.  0.5 H
4.  0.05 H

The figure shows a battery with emf 15V in a circuit with ${\mathrm{R}}_1=30\mathrm{\Omega }, {\mathrm{R}}_2=10\mathrm{\Omega }, {\mathrm{R}}_3=20\mathrm{\Omega } \mathrm{and} \mathrm{L}=3.0 \mathrm{H}.$ The switch S is initially in the open position and is then closed at time t=0. Then the graph which shows the correct variation of current through battery after switch S is closed.
                                     
1.                        2.
3.                   4.

Given the circuit above, which of these choices is a possible system of equations representing the complete Kirchoff's law description of the circuit?
                       
1.  $\left\{\begin{array}{l}{\mathrm{V}}_{\mathrm{b}}={\mathrm{I}}_1\mathrm{R}\\ \mathrm{Q}={\mathrm{CV}}_{\mathrm{b}}\\ {\mathrm{V}}_{\mathrm{b}}=-\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{at}}\end{array}\right.$                                2.  $\left\{\begin{array}{l}{\mathrm{V}}_{\mathrm{b}}-\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{dt}}-{\mathrm{RI}}_1=0\\ -\frac{\mathrm{Q}}{\mathrm{C}}-\mathrm{R}\left({\mathrm{I}}_1-{\mathrm{I}}_2\right)+\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{dt}}=0\\ {\mathrm{I}}_3={\mathrm{I}}_1-{\mathrm{I}}_2\end{array}\right.$
3.  $\left\{\begin{array}{l}{\mathrm{V}}_{\mathrm{b}}-\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{dt}}-{\mathrm{RI}}_2=0\\ -\mathrm{QC}-\mathrm{R}\left({\mathrm{I}}_1+{\mathrm{I}}_2\right)+\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{dt}}=0\end{array}\right.$           4.  $\left\{\begin{array}{l}{\mathrm{V}}_{\mathrm{b}}-\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{dt}}+{\mathrm{RI}}_1=0\\ -\frac{\mathrm{Q}}{\mathrm{C}}-{\mathrm{RI}}_3-\mathrm{L}\frac{{\mathrm{dI}}_2}{\mathrm{dt}}=0\\ {\mathrm{I}}_1={\mathrm{I}}_2+{\mathrm{I}}_3\end{array}\right.$

Switch S is closed for a long time at t=0. If it is opened, then:
                         
1.  total heat produced in resistor R after opening the switch is $\frac{1}{2}\frac{\mathrm{LV}}{{\mathrm{R}}^2}$
2.  total heat produced in resistor ${\mathrm{R}}_1$ after opening the switch is $\frac{1}{2}\frac{{\mathrm{LV}}^2}{{\mathrm{R}}^2}\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_1+{\mathrm{R}}_2}\right)$
3.  heat produced in resistor ${\mathrm{R}}_1$ after opening the switch is $\frac{1}{2}\frac{{\mathrm{R}}_2{\mathrm{LV}}^2}{\left({\mathrm{R}}_1+{\mathrm{R}}_2\right){\mathrm{R}}^2}$
4.  no heat will be produced in ${\mathrm{R}}_1$

The frequency of oscillation of current in the inductance is:
                                       
1.  $\frac{1}{3\sqrt{\mathrm{LC}}}$
2.  $\frac{1}{6\mathrm{\pi }\sqrt{\mathrm{LC}}}$
3.  $\frac{1}{\sqrt{\mathrm{LC}}}$
4.  $\frac{1}{2\mathrm{\pi }\sqrt{\mathrm{LC}}}$

Resonance occurs in a series L-C-R circuit when the frequency of the applied e.m.f. is 1000 Hz. Then:
1.  when f=900 Hz, the circuit behaves as a capacitive circuit
2.  the impendence of the circuit is maximum at f=1000 Hz
3.  at resonance the voltages across L and current in C differ in phase by 180$°$
4.  if the value of C is doubled resonance occurs at f=2000 Hz

A coil of inductance 5H is joined to cell of emf 6V through a resistance 10$\mathrm{\Omega }$ at time t=0. The emf across the coil at time t=ln $\sqrt{2}$ s is:
1.  3 V
2.  1.5 V
3.  0.75 V
4.  4.5 V

The circuit has been operating for a long time. The instant after the switch in the circuit labelled S  is opened, what is the voltage across the inductor V_L and which labelled point (A or B) of the inductor is at a higher potential? Take ${\mathrm{R}}_1=4.0 \mathrm{\Omega }, {\mathrm{R}}_2=8.0 \mathrm{\Omega } \mathrm{and} \mathrm{L}=2.5\mathrm{H}.$
                               
1.  V_L = 12V; Point A is at the higher potential
2.  V_L = 12V; Point B is at the higher potential
3.  V_L = 6V; Point A is at the higher potential
4.  V_L = 6V; Point B is at the higher potential

A series circuit has a resistance of 60$\mathrm{\Omega }$ and an impedance of 135$\mathrm{\Omega }$. When the total potential difference is 120V, the power consumed in the circuit will be:
1.  47.4 W
2.  95 W
3.  zero
4.  52.3 W