A micro-ammeter has a resistance of $100 \mathrm{\Omega }$ and full scale range of $50 \mathrm{\mu A}$. It can be used as a voltmeter and an ammeter of a higher range provided a resistance is added to it. Pick the correct range and resistance combination (s).

Two cells of unequal emfs ${\epsilon }_1$ and ${\epsilon }_2$ and internal resistances $r_1$ and $r_2$are joined as shown. $V_A$ and $V_B$ are the potentials at $A$ and $B$, respectively. 

In the potentiometer arrangement shown, the driving cell $D$ has emf $\epsilon$ and internal resistance $r$. The cell $C$, whose emf is to be measured, has emf $\frac{\epsilon }{2}$ and internal resistance $2r$. The potentiometer wire is the potentiometer wire is $100-\mathrm{cm}$ long. If balance is obtained at the length $AJ=l.$

In the circuit shown below, the key is pressed at time $t= 0.$ Which of the following statement(s) is (are) true?

The figure shows an experimental plot discharging of a capacitor in an $RC$ circuit. The time constant $\tau$ of this circuit lies between