David Sang and Graham Jones Solutions for Chapter: Practical Skills at A Level, Exercise 6: Questions

The values of load shown in table are given without any indication of their uncertainties. Suggest a reason for this.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

A graph is plotted with $\ln R$ on the $y$ -axis and $\ln r$ on the $x$ -axis. Express the gradient and $y$ -intercept in terms of $a \& b$.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

 Values of $r \& R$ measured in an experiment are given in Table.

Copy and complete the table by calculating and recording values of $\ln (r/\mathrm{mm})$ and $\ln (R/\Omega )$ and include the absolute uncertainties in $\ln (r/\mathrm{mm})$

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

 Plot a graph of $\ln (r/\mathrm{mm})$ against $\ln (R/\Omega )$. Include error bars for $\ln (r/\mathrm{mm})$.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

 Draw the line of best fit and a worst acceptable straight line on your graph.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

Determine the gradient of the line of best fit. Include the uncertainty in your answer.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

Determine the value of $b$ according to the best fit line.

A student measures the radius $r$ and the resistance $R$ of several equal lengths of wire. The results are shown in Table. It is suggested that $R$ and $r$ are related by the equation: $R=a{r}^b$

Where $a \&\hspace{0.17em}b$ are constants.

Determine the value of $a$ and its uncertainty.