The initial rate of increase of current when a battery of emf $6 \, V$ is connected in series with an inductance of $2 \, H$ and resistance of $12 \, \Omega$ is

An ideal coil of $10 \ H$ is connected in series with a resistance of $5 \ \Omega$ and a battery of $5 \ V$. $2 \ s$ after the connection is made,the current flowing in the circuit in amperes is:

In the figure below,the switches $S_1$ and $S_2$ are closed simultaneously at $t=0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) $V$ and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{\max}$ at time $t=T$. Which of the following statements is (are) true?
$(A)$ $I_{\max}=\frac{V}{2R}$
$(B)$ $I_{\max}=\frac{V}{4R}$
$(C)$ $T=\frac{L}{R} \ln 2$
$(D)$ $T=\frac{2L}{R} \ln 2$

$A$ constant voltage of $25 \, V$ is applied to a series $L-R$ circuit at $t=0$ by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?

For $L-R$ circuit,the time constant is equal to

Find the current in the sliding rod $AB$ (resistance $= R$) for the arrangement shown in the figure. $\vec{B}$ is constant and is directed out of the paper. The parallel wires have no resistance. $v$ is constant. The switch $S$ is closed at time $t = 0$.