Question

What is the ${\mathbf{emf}}_{\mathbf{x}}$of a cell being measured in a potentiometer, if the standard cell’s emf is 12.0 Vand the potentiometer balances for${\mathbf{R}}_{\mathbf{x}}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{000}\mathbf{}\mathbf{\Omega }$and ${\mathbf{R}}_{\mathbf{s}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{500}\mathbf{}\mathbf{\Omega }$?

Short answer

The of a cell being measured in a potentiometer is ${\mathrm{E}}_{\mathrm{x}}=24.0\mathrm{V}$.

Step-by-step solution

Concept Introduction

The electric potential generated by an electrochemical cell or a changing magnetic field is known as electromotive force. Electromotive force (EMF) is a well-known abbreviation.

Information Provided

• Emf of a standard cell: ${\mathrm{E}}_{\mathrm{s}}=12\mathrm{V}$
• Resistance of the potentiometer:$R_x=5\Omega$
• Standard resistance value:${\mathrm{R}}_{\mathrm{s}}=2.5\mathrm{\Omega }$

Calculation for EMF of the cell

Calculate ${\mathrm{emf}}_{\mathrm{x}}$, of a cell using a potentiometer. The formula is -

$$\begin{gathered} {\mathrm{E}}_{\mathrm{x}}={\mathrm{E}}_{\mathrm{s}}\frac{{\mathrm{R}}_{\mathrm{x}}}{{\mathrm{R}}_{\mathrm{s}}} \\ =(12\mathrm{V})\frac{5\mathrm{\Omega }}{2.5\mathrm{\Omega }} \\ =12\mathrm{V}\times 2.0 \\ =24.0\mathrm{V} \end{gathered}$$

Therefore, the value for emf is ${\mathrm{E}}_{\mathrm{x}}=24.0\mathrm{V}$.