In the potentiometer arrangement (figure), the driving cell $A$ has emf $\epsilon$and internal resistance $r$. The emf of the cell $B$ is to be rechecked has emf $\frac{\mathrm{\epsilon }}{2}$ and internal resistance $2r$. The potentiometer wire $CD$ is $100 \mathrm{cm}$ long. If balance is obtained, the length $CJ=l$ is,

In a practical Wheatstone bridge circuit (figure), when one more resistance of $100 \mathrm{\Omega }$ is connected in parallel with unknown resistance $x$, then the ratio $\frac{l_1}{l_2}$ becomes $2$. $l_1$ is the balance length and $AB$ is a uniform wire. Then, the value of $x$ must be,

Two ideal batteries having emf $E_1$, and $E_2$ are connected as shown in the figure. The values of resistances are chosen in such a way that the ammeter reading is zero. The reading of the voltmeter will be (consider the meters to be ideal)

The figure shows a meter bridge set up with null deflection in the galvanometer. The value of the unknown resistor $R$ is

In the given arrangement, the reading of ammeter is same in each case when either $K_1$ or $K_2$ is closed. The reading of the ammeter is,