A $10 \mathrm{m}$ long potentiometer wire carries a steady current. $\mathrm{A}$ $1.018 \mathrm{V}$ standard cell is balanced at a length of $850 \mathrm{cm}$. Find the maximum emf that can be measured.

In the circuit shown in the figure, a voltmeter reads $30 \mathrm{V}$ when it is connected across the $400 \mathrm{\Omega }$ resistance. Calculate what the same voltmeter will read when it is connected across the $300 \mathrm{\Omega }$ resistance.

The galvanometer in each of the two given circuits, Figure does not show any deflection. Find the ratio of resistors ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ used in their circuits.

Calculate the value of $\mathrm{R}$ in the balance condition of the Wheatstone bridge, if the carbon resistor connected across the arm $\mathrm{C} \mathrm{D}$ has the colour sequence red, red and orange as shown in the figure, Fig. If now the resistance of the arms $\mathrm{B} \mathrm{C}$ and $\mathrm{C} \mathrm{D}$ are interchanged, to obtain the balance condition, another carbon resistor is connected in place of $\mathrm{R}$. What now be the sequence of colour bands of the carbon resistor?

Two cells of emfs ${\mathrm{ϵ}}_1$ and ${\in }_2\left({\mathrm{ϵ}}_1>{\mathrm{ϵ}}_2\right)$ are connected as shown in Fig. When a potentiometer is connected between $\mathrm{A}$ and $\mathrm{B}$, the balancing length of the potentiometer wire is $3.00 \mathrm{m}$. on connecting the same potentiometer between $\mathrm{A}$ and $\mathrm{C},$ the balancing length is $1.00 \mathrm{m}.$ Calculate the ratio of ${\mathrm{ϵ}}_1$ and ${\mathrm{ϵ}}_2$.