Two inductors $L_1$ (inductance $1 \text{ mH}$,internal resistance $3 \text{ } \Omega$) and $L_2$ (inductance $2 \text{ mH}$,internal resistance $4 \text{ } \Omega$),and a resistor $R$ (resistance $12 \text{ } \Omega$) are all connected in parallel across a $5 \text{ V}$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum to the minimum current $(I_{\max} / I_{\min})$ drawn from the battery is:

The diagram below shows two coils $A$ and $B$ placed parallel to each other at a very small distance. Coil $A$ is connected to an ac supply. $G$ is a very sensitive galvanometer. When the key $K$ is closed:

Which of the following statements is incorrect?

$A$ small bar magnet of dipole moment $M$ is moving with speed $v$ along the $x$-direction towards a small closed circular conducting loop of radius $a$ with its centre $O$ at $x=0$ (see figure). Assume $x >> a$ and the coil has a resistance $R$. Which of the following statement$(s)$ is/are true?

The unit $\text{Wb}/\Omega$ represents which physical quantity?

$A$ conducting square loop initially lies in the $XZ$ plane with its lower edge hinged along the $X$-axis. Only in the region $y \geq 0$,there is a time-dependent magnetic field pointing along the $Z$-direction,$\vec{B}(t) = B_0(\cos \omega t) \hat{k}$,where $B_0$ is a constant. The magnetic field is zero everywhere else. At time $t=0$,the loop starts rotating with constant angular speed $\omega$ about the $X$-axis in the clockwise direction as viewed from the $+X$ axis (as shown in the figure). Ignoring self-inductance of the loop and gravity,which of the following plots correctly represents the induced e.m.f. $(V)$ in the loop as a function of time?