In the circuit shown,$X$ is joined to $Y$ for a long time,and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

Two resistors of $10\, \Omega$ and $20\, \Omega$ and an ideal inductor of $10\, H$ are connected to a $2\, V$ battery as shown. The key $K$ is inserted at time $t = 0$. The initial $(t = 0)$ and final $(t \rightarrow \infty)$ currents through the battery are

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 which of the following circuits is the current maximum just after the switch $S$ is closed?

An $e.m.f.$ of $15 \ V$ is applied in a circuit containing $5 \ H$ inductance and $10 \ \Omega$ resistance. The ratio of the currents at time $t = \infty$ and at $t = 1 \ s$ is:

An inductor of $10\, \text{mH}$ is connected to a $20\, \text{V}$ battery through a resistor of $10\, \text{k}\Omega$ and a switch. After a long time,when maximum current is set up in the circuit,the current is switched off. The current in the circuit after $1\, \mu\text{s}$ is $\frac{x}{100}\, \text{mA}$. Then $x$ is equal to ...... . (Take $e^{-1} = 0.37$)