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The figure shows the variation of R, X_L, and X_C with frequency f in a series of L, C, and R circuits. For which frequency point is the circuit inductive?

The diagram shows a capacitor C and a resistor R connected in series to an ac source. V₁ and V₂ are voltmeters and A is an ammeter.
   
Consider now the following statements

Which of these statements is/are correct?

 
A thin semicircular conducting ring (PQR) of radius 'r' is falling with its plane vertical in a horizontal magnetic field B, as shown in figure. The potential difference developed across the ring when its speed is v is: 

1. Zero
2. $Bv{\mathrm{\pi r}}^2/2$ and P is at the higher potential
3. $\mathrm{\pi rBv}$ and R is at the higher potential
4. 2BvR and R is at the higher potential

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\frac{dB}{dt}$. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of the magnetic field as shown in the figure. Then, the emf generated is:
       
1.  Zero in loop 1 and zero loop 2
2.  $-\frac{dB}{dt}\pi r^2$ in loop 1 and zero in loop 2
3.  $-\frac{dB}{dt}\pi R^2$ in loop 1 and zero in loop 2
4.  Zero in loop 1 and not defined in loop 2

The key K is inserted at time t= 0. The initial (t=0) and final $\left(t\to \infty \right)$ currents through battery are :

1. $\frac{1}{15}Amp, \frac{1}{10}Amp$
2. $\frac{1}{10}Amp, \frac{1}{15}Amp$
3. $\frac{2}{15}Amp, \frac{1}{10}Amp$
4. $\frac{1}{15}Amp, \frac{2}{25}Amp$

An electron moves on a straight-line path XY as shown. The abcd is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil? 
,
1. abcd
2. adcb
3. The current will reverse its direction as the electron goes past the coil
4. No current included

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux ϕ linked with the primary coil is given by ϕ=${\varphi }_0$+4t, where ϕ is in weber, t is time in second and ϕ₀is a constant, the output voltage across the secondary coil is:
1. 90 V
2. 120 V
3. 220 V
4. 30 V

While keeping area of cross-section of a solenoid same, the number of turns and length of solenoid one both doubled. The self inductance of the coil will be
1. halved
2. doubled
3. $\frac{1}{4}$ times the original value
4. unaffected 

For a transparent medium, relative permeability and permittivity, ${\mu }_r$ $and$ ${\epsilon }_r$ are 1.0 and 1.44 respectively. The velocity of light in this medium would be:
1. 2.5$\times {10}^8$ m/s
2. 3 $\times {10}^8$ m/s
3. 2.08 $\times {10}^8$ m/s
4. 4.32 $\times {10}^8$ m/s

The intensity of visible radiation at a distance of 1 m from a bulb of 100 W which converts only 5% its power into light is :
(1) 0.4 $W/m^2$             (2) 0.5 $W/m^2$
(3) 0.1 $W/m^2$             (4) 0.01 $W/m^2$

The charge of a parallel plate capacitor is varying as $q=q_0 \sin \omega t$.  Then find the magnitude of displacement current through the capacitor.  (Plate Area = A, separation of plates = d)
(1) $q_0 \cos \left(\omega t\right)$                      (2) $q_0\omega \sin \omega t$
(3) $q_0\omega \cos \omega t$                     (4) $\frac{q_{0}A\omega }{d}\cos \omega t$

The energy density of the electromagnetic wave in vacuum is given by the relation
(1) $\frac{1}{2}.\frac{E^2}{{\epsilon }_0}+\frac{B^2}{2{\mu }_0}$                 (2) $\frac{1}{2}{\epsilon }_0{E}^2+\frac{1}{2}{\mu }_0{B}^2$
(3) $\frac{E^2+B^2}{C}$                           (4) $\frac{1}{2}{\epsilon }_0{E}^2+\frac{B^2}{2{\mu }_0}$

An inductor 20 mH, a capacitor 100 μF, and a resistor 50 $\Omega$ are connected in series across a source of emf, V= 10sin314t. The power loss in the circuit is:
1. 0.79 W
2. 0.43 W
3. 2.74 W
4. 1.13 W

An alternating voltage source is connected to a series R-C circuit. Consider two situations:

If the current through the resistor is I and the voltage across the capacitor is V, then:
1. \(V_a < V_b\)
2. \(V_a > V_b\)
3. \(i_a > i_b\)
4. \(V_a = V_b\)

In a certain circuit current changes with time according to $\mathrm{i}=2\sqrt{\mathrm{t}}$. Root mean square value of current between t=2 to t=4s will be:-
1.  $\sqrt{2}\mathrm{A}$
2.  $2\mathrm{A}$
3.  $2\sqrt{3}\mathrm{A}$
4.  $130 \mathrm{V}$