Find value of time constant in the following circuit.

In the given circuit at $t=0, S$ is closed, then at time $t, \frac{i_1}{i_2}$

 The resistances $500\mathrm{\Omega }$ and $1000\mathrm{\Omega }$ are connected in series with a battery of $1.5 \mathrm{V}$. The voltage across the $1000\mathrm{\Omega }$ resistance is measured by a voltmeter having a resistance of $1000\mathrm{\Omega }$. The reading in voltmeter would be

The current through $2\mathrm{\Omega }$ will be

The diagram shows a modified meter bridge, which is used for measuring two unknown resistances at the same time, when the first Galvanometer is used for obtaining the balanced point, it is found at point $C.$ Now the first galvanometer is removed and the $2\mathrm{nd}$ galvanometer is used which gives balance point at $D.$ Use the details given in diagram, $AB=L,AC=\frac{L}{4},AD=\frac{2L}{3}.$ The value of resistances $R_1$ and $R_2$ are respectively

In the circuit shown, switches $S_1$ and $S_2$ have been closed for a long time