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Here's how to solve the problem using the potentiometer principle:

Identify the given values.
The electromotive force (e.m.f.) of the standard cell is $E_1 = 1.50 \text{ V}$ .
The balance length for the standard cell is $L_1 = 52 \text{ cm}$ .
The e.m.f. of the unknown dry cell is $E_2 = E$ .
The balance length for the unknown dry cell is $L_2 = 75 \text{ cm}$ .
Apply the potentiometer principle.
For a potentiometer, the e.m.f. of a cell is directly proportional to its balance length. This relationship can be expressed as:
$\frac{E_1}{E_2} = \frac{L_1}{L_2}$
Substitute the known values into the formula.
$\frac{1.50 \text{ V}}{E} = \frac{52 \text{ cm}}{75 \text{ cm}}$
Solve for $E$ .
To find $E$ , rearrange the equation:
$E = 1.50 \text{ V} \times \frac{75 \text{ cm}}{52 \text{ cm}}$ $E = 1.50 \times \frac{75}{52} \text{ V}$ $E = 1.50 \times 1.442307... \text{ V}$ $E = 2.16346... \text{ V}$
Round the answer to an appropriate number of significant figures.
Rounding to three significant figures (consistent with 1.50 V):
$E = \boxed{\text{2.16 V}}$

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