The total length of the wire of a potentiometer is 1.0 m. A potential gradient of 0.0015 V/cm is obtained when a steady current is passed through this wire. Calculate, (i) the distance of the null point on connecting standard cell of 1.018 V. (ii) the unknown p.d. if the null point is obtained ata distance of 940 cm, and (iii) the maximum p.d. which can be measured by this instrument.

The total length of the wire of a potentiometer is 1.0 m. A potential gradient of 0.0015 V/cm is obtained when a steady current is passed through this wire. Calculate,
(i) the distance of the null point on connecting standard cell of 1.018 V.
(ii) the unknown p.d. if the null point is obtained ata distance of 940 cm, and
(iii) the maximum p.d. which can be measured by this instrument.
Solution:
Given,
length of potentiometer wire, \(L\) = 10 m
potential gradient, \(k\) = 0.0015 V/cm = 0.15 V/m

(i) \(l\) = ?, \(E\) = 1.018 V
For null point, potential across potentiometer wire should be equal to that of standard cell.
\[\begin{align*} V&=E=kl \\ 1.018&=0.15 \times l\\ \therefore l&=6.78 \hspace{0.1cm} m\\ \end{align*}\]
(ii) \(l\) = 940 cm = 9.40 m , \(V\) = ?
\[\begin{align*} V&=kl\\ &=0.15 \times 9.40\\ &=1.41 \hspace{0.1cm} V\\ \end{align*}\]
(iii) Maximum potential difference is found for total length of potentiometer wire.
\[\begin{align*} V_{max}&=kL\\ &=0.15 \times 10\\ \therefore V_{max}&=1.5 \hspace{0.1cm} V\\ \end{align*}\]