2 questions from 2024
The circuit shown in the figure contains an inductor \( L \), a capacitor \( C_0 \), a resistor \( R_0 \) and an ideal battery. The circuit also contains two keys \( K_1 \) and \( K_2 \). Initially, both the keys are open and there is no charge on the capacitor. At an instant, key \( K_1 \) is closed and immediately after this the current in \( R_0 \) is found to be \( I_1 \). After a long time, the current attains a steady state value \( I_2 \). Thereafter, \( K_2 \) is closed and simultaneously \( K_1 \) is opened and the voltage across \( C_0 \) oscillates with amplitude \( V_0 \) and angular frequency \( \omega_0 \).
Match the quantities mentioned in List-I with their values in List-II and choose the correct option. 
A region in the form of an equilateral triangle (in \( x\text{-}y \) plane) of height \( L \) has a uniform magnetic field \( \\vec{B} \) pointing in the \( +z \)-direction. A conducting loop \( PQR \), in the form of an equilateral triangle of the same height \( L \), is placed in the \( x\text{-}y \) plane with its vertex \( P \) at \( x = 0 \) in the orientation shown in the figure. At \( t = 0 \), the loop starts entering the region of the magnetic field with a uniform velocity \( \\vec{v} \) along the \( +x \)-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graph best depicts the variation of the induced emf \( (E) \) in the loop as a function of the distance \( (x) \) starting from \( x = 0 \)?
