Potential Difference Between Two Points — Question 6

Question 6

A potentiometer compares emfs without drawing current from the test cell at null

A uniform resistive wire has a constant voltage gradient g. A reference cell of emf 1.20 V balances at length .600 m; an unknown cell balances at .850 m under the same wire current. At balance, detector current is zero.

1. Find g and the unknown emf.

2. If both cells have finite internal resistance, show why those resistances do not affect the ideal null comparison.

Question 6 - Solution

A potentiometer compares emfs without drawing current from the test cell at null

(a) Method and calculation

$$\mathcal E_{\mathrm{ref}}=g\ell_{\mathrm{ref}}\Rightarrow g=1.20/.600=2.00\,\mathrm{V/m}.$$$$\mathcal E_x=g\ell_x=(2.00)(.850)=1.70\,\mathrm V.$$

(b) Interpretation and further calculation

$$I_{\mathrm{cell}}=0\Rightarrow V_{\mathrm{terminal}}=\mathcal E-I_{\mathrm{cell}}r=\mathcal E.$$$$\mathcal E_x/\mathcal E_{\mathrm{ref}}=\ell_x/\ell_{\mathrm{ref}}=.850/.600.$$

Physical check

A null method reads the open-circuit emf; a finite-current measurement generally reads a lower discharge terminal voltage.