Question

Match the statement in column I with the results in column II
$\begin{array}{ccc}\text{Column- I}& \text{Column - II}& \\ \text{(A) A variable resistor is connected across a non ideal}& \text{(P) First increases for some time}& \\ \text{cell. As the variable resistor is}& \text{and then decreases}& \\ \text{continuously increased from zero to a very}& & \\ \text{large value, the electric power consumed}& & \\ \text{by the variable resistor}& & \\ \text{(B) A circular ring lies in space having}& \text{(Q) First decreases for some time}& \\ \text{uniform and constant magnetic field which}& \text{and then increases}& \\ \text{is parallel to plane of the ring. Keeping the}& & \\ \text{centre of ring fixed, the rings is rotated by}& & \\ {180}^{\circ }\text{about one of its diameter which is}& & \\ \text{perpendicular to magnetic field with}& & \\ \text{constant angular speed. For the duration}& & \\ \text{the ring rotates, the magnitude of induced}& & \\ \text{emf in the ring}& & \\ \text{(C) A thin rod of length 1 cm lies along}& \text{(R) is always constant}& \\ \text{principal axis of a convex lens of focal}& & \\ \text{length 5 cm. One end of rod is at a distance}& & \\ \text{10 cm from optical centre of the lengs. The}& & \\ \text{convex lens is moved (without rotation)}& & \\ \text{perpendicular to initial principal axis by}& & \\ \text{5 mm and brought back to its initial}& & \\ \text{position. Length of image of the rod}& & \\ & & \\ \text{(D) A bulb (of negiligible inductance) and a}& \text{(S) increases or may increase}& \\ \text{capacitor in series are connected across an}& \text{over some time interval.}& \\ \text{ideal AC source of constant peak voltage}& & \\ \text{and variable frequency. As frequency of AC}& & \\ \text{source is continuously increased, the}& & \\ \text{brightness of bulb}& & \end{array}$

• A. A-P, Q; B - Q, S; C - P, S; D- P,S
• B. A-P,S; B-Q,S; C-P,S; D-S
• C. A-P,S; B-Q,S; C-P,Q; D-Q,S
• D. A-P; B-S; C-P,S; D-R

Answer 1

The correct option is A A-P, Q; B - Q, S; C - P, S; D- P,S

(A) A the plot of power P consumed by variable resistor of resistance R w.r.t R when connected across a non-ideal cell is given by

(B) At the instant ring has rotated by $q=\omega t$ ($\omega$ = angular speed) in uniform and constant magnetic field B, the magnetic flux through the ring is $\varphi =BA\sin \omega t$ or $EMF=\frac{d\varphi }{dt}=BA\cos \omega t$
Hence for first half cycle, magnitude of emf first decreases and then increases.
(C) As the lens is moved up, the projection of length of image on principal axis remains same, but its slant with principal axis increases. This increase is due to the fact that lateral magnification of each point of image of rod is different. Hence as lens moves up the size of image increase and when it moves down the size of images decreases.
(D) as frequency of ac source increases, reactance of capacitor decreases. Therefore, the bulb glows more brighter.