Draw the pattern of the magnetic field lines for the two parallel straight conductors carrying current of same magnitude 'I' in opposite directions as shown. Show the direction of magnetic field at a point O which is equidistant from the two conductors. (Consider that the conductors are inserted normal to the plane of a rectangular cardboard.)
When two conductors carry currents in opposite directions, the magnetic field produced by each conductor at any point in space will be in opposite directions. For conductors with current flowing in opposite directions, the field lines will be arranged such that:
- For the first conductor (current flowing in one direction), the magnetic field lines will circle the conductor in a clockwise direction (if viewed from above).
- For the second conductor (current flowing in the opposite direction), the magnetic field lines will circle the conductor in a counterclockwise direction. At a point \( O \), which is equidistant from both conductors, the magnetic field contributions from both conductors will cancel out if the currents are of equal magnitude and flow in opposite directions. The field lines will form circular loops around each conductor, with opposite directions of field due to opposite current directions.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below:
Figure shows a current carrying square loop ABCD of edge length is $ a $ lying in a plane. If the resistance of the ABC part is $ r $ and that of the ADC part is $ 2r $, then the magnitude of the resultant magnetic field at the center of the square loop is: 
Find the mean and mode of the following data:
| Class | 15--20 | 20--25 | 25--30 | 30--35 | 35--40 | 40--45 |
| Frequency | 12 | 10 | 15 | 11 | 7 | 5 |