21.5 Null Measurements

This equation is used to calculate the unknown resistance when current through the galvanometer is zero. This method can be very accurate (often to four significant digits), but it is limited by two factors. First, it is not possible to get the current through the galvanometer to be exactly zero. Second, there are always uncertainties in $R_{1}$, $R_{2}$, and $R_{3}$, which contribute to the uncertainty in $R_{x}$.

Identi…

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

When an unknown resistance $R_{\text{x}}$ is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting $R_{3}$ to be $\text{2500} \Omega$. What is $R_{\text{x}}$ if $\frac{R_{2}}{R_{1}} = 0 . \text{625}$?

(a) What is the unknown $\text{emf}_{\text{x}}$ in a potentiometer that balances when $R_{\text{x}}$ is $\text{10} . 0 \Omega$, and balances when $R_{\text{s}}$ is $\text{15} . 0 \Omega$ for a standard 3.000-V emf? (b) The same $\text{emf}_{\text{x}}$ is placed in the same potentiometer, which now balances when $R_{\text{s}}$ is $\text{15} . 0 \Omega$ for a standard emf of 3.100 V. At what resistance $R_{\text{x}}$ will the potentiometer balance?

Suppose you want to measure resistances in the range from $\text{10} . 0 \Omega$ to $\text{10} . 0 kΩ$ using a Wheatstone bridge that has $\frac{R_{2}}{R_{1}} = 2 . \text{000}$. Over what range should $R_{3}$ be adjustable?