Current electricity

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Question 75

Medium

This question is based on a practical method to determine the resistivity of a metal wire, Z.

The diameter of wire Z is measured using a micrometer screw gauge. The main scale has a resolution of $mm0.50\text{ mm}$ . The edge of the thimble is positioned between the $mm0.50\text{ mm}$ mark and the $mm1.00\text{ mm}$ mark on the main scale, and the $30$ division on the thimble scale is aligned exactly with the horizontal datum line. Since each division on the thimble scale represents $mm0.01\text{ mm}$ , state the diameter $d$ of wire Z in mm.

[1]

In an experiment to find the resistance per unit length of wire Z, a series resistor of resistance $Ω3.3\ \Omega$ is connected in series with a cell, a switch, and wire Z.

With the switch closed, the potential difference across the $Ω3.3\ \Omega$ resistor is $V1.98\text{ V}$ .
The switch is opened, and the voltmeter is reconnected across a length $0.600\text{ m}$ of wire Z.
When the switch is closed again, the potential difference across this length of wire is $V1.08\text{ V}$ .

Show that the resistance $R$ of the wire between the voltmeter clips is approximately $Ω1.8\ \Omega$ .

[3]

The student determines the resistance $R$ for several different lengths $L$ of wire Z and plots a graph of $R$ against $L$ . The gradient of this graph (the resistance per metre of wire Z) is $m−13.03\ \Omega\text{ m}^{-1}$ .

Table 1 shows the manufacturer's values for the resistance per metre of four different metals at various wire diameters $d$ .

Diameter $d$ / mm	Brass / $m−1\Omega\text{ m}^{-1}$	Constantan / $m−1\Omega\text{ m}^{-1}$	Stainless Steel / $m−1\Omega\text{ m}^{-1}$	Nichrome / $m−1\Omega\text{ m}^{-1}$
$0.40$	$0.636$	$3.90$	$5.49$	$11.9$
$0.60$	$0.283$	$1.73$	$2.44$	$5.31$
$0.80$	$0.159$	$0.975$	$1.37$	$2.98$

(i) Identify the metal used for wire Z. (ii) Determine the resistivity $ρ\rho$ of this metal. State an appropriate SI unit for your answer.

[5]

The student adds error bars for $R$ and $L$ to each plotted point. She estimates that:

each value of $R$ has a percentage uncertainty of $4%4\%$
each value of $L$ has an absolute uncertainty of $mm5\text{ mm}$

Compare her error bars for the point at $150\text{ mm}$ (where $0.45\ \Omega$ ) with her error bars for the point at $600\text{ mm}$ (where $1.80\ \Omega$ ).

[3]

Current electricity

Question 75

Medium

This question is based on a practical method to determine the resistivity of a metal wire, Z.

[1]

In an experiment to find the resistance per unit length of wire Z, a series resistor of resistance $Ω3.3\ \Omega$ is connected in series with a cell, a switch, and wire Z.

With the switch closed, the potential difference across the $Ω3.3\ \Omega$ resistor is $V1.98\text{ V}$ .
The switch is opened, and the voltmeter is reconnected across a length $0.600\text{ m}$ of wire Z.
When the switch is closed again, the potential difference across this length of wire is $V1.08\text{ V}$ .

Show that the resistance $R$ of the wire between the voltmeter clips is approximately $Ω1.8\ \Omega$ .

[3]

Table 1 shows the manufacturer's values for the resistance per metre of four different metals at various wire diameters $d$ .

Diameter $d$ / mm	Brass / $m−1\Omega\text{ m}^{-1}$	Constantan / $m−1\Omega\text{ m}^{-1}$	Stainless Steel / $m−1\Omega\text{ m}^{-1}$	Nichrome / $m−1\Omega\text{ m}^{-1}$
$0.40$	$0.636$	$3.90$	$5.49$	$11.9$
$0.60$	$0.283$	$1.73$	$2.44$	$5.31$
$0.80$	$0.159$	$0.975$	$1.37$	$2.98$

(i) Identify the metal used for wire Z. (ii) Determine the resistivity $ρ\rho$ of this metal. State an appropriate SI unit for your answer.

[5]

The student adds error bars for $R$ and $L$ to each plotted point. She estimates that:

each value of $R$ has a percentage uncertainty of $4%4\%$
each value of $L$ has an absolute uncertainty of $mm5\text{ mm}$

Compare her error bars for the point at $150\text{ mm}$ (where $0.45\ \Omega$ ) with her error bars for the point at $600\text{ mm}$ (where $1.80\ \Omega$ ).

[3]

Current electricity

Question 75

Current electricity Questions

Current electricity

Question 75

Current electricity Questions