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(b) (i) What is meant by electrical resistivity of a material ?
(ii) A series electric circuit comprising a resistor made of a metallic wire has an ammeter which reads $300\ \text{mA}$. If the length of the wire is made three times, what will be the new reading in the ammeter ?
(iii) Calculate the resistance of a $500\ \text{m}$ long aluminium wire of cross-sectional area $1\times10^{-3}\ \text{m}^2$ and resistivity $$\begin{aligned}& 2.65\times10^{-8} \\ & \Omega\text{m}\end{aligned}$$.
(ii) A series electric circuit comprising a resistor made of a metallic wire has an ammeter which reads $300\ \text{mA}$. If the length of the wire is made three times, what will be the new reading in the ammeter ?
(iii) Calculate the resistance of a $500\ \text{m}$ long aluminium wire of cross-sectional area $1\times10^{-3}\ \text{m}^2$ and resistivity $$\begin{aligned}& 2.65\times10^{-8} \\ & \Omega\text{m}\end{aligned}$$.
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(b)
(i) Electrical resistivity is the resistance offered by a wire of length 1m and
area of cross-section 1m$^2$ (1)
(ii) $\text{V=IR}$
$\text{V = 300 \times R}$ -----------(1)
$\text{R} \propto \text{l}$
$\text{R1 = 3 \times R}$ ($\frac{1}{2}$)
$\text{V = I1 R1}$
$\text{V = I1 \times 3 R}$ -----------(2)
$\text{From (1) and (2)}$
$\text{I1 \times 3 R = 300 \times R}$
$\text{I1 = 100 mA (Reading of ammeter)}$ ($\frac{1}{2}$)
(iii) $\text{R} = \rho \frac{\text{l}}{\text{A}}$ (1)
$\text{R} = \frac{2.65 \times 10^{-8} \times 500}{1 \times 10^{-3}}$ ($\frac{1}{2}$)
$\text{R} = 2.65 \times 5 \times 10^{-3} \text{ \Omega}$
$\text{R} = 13.25 \times 10^{-3} \text{ \Omega}$ ($\frac{1}{2}$)
(i) Electrical resistivity is the resistance offered by a wire of length 1m and
area of cross-section 1m$^2$ (1)
(ii) $\text{V=IR}$
$\text{V = 300 \times R}$ -----------(1)
$\text{R} \propto \text{l}$
$\text{R1 = 3 \times R}$ ($\frac{1}{2}$)
$\text{V = I1 R1}$
$\text{V = I1 \times 3 R}$ -----------(2)
$\text{From (1) and (2)}$
$\text{I1 \times 3 R = 300 \times R}$
$\text{I1 = 100 mA (Reading of ammeter)}$ ($\frac{1}{2}$)
(iii) $\text{R} = \rho \frac{\text{l}}{\text{A}}$ (1)
$\text{R} = \frac{2.65 \times 10^{-8} \times 500}{1 \times 10^{-3}}$ ($\frac{1}{2}$)
$\text{R} = 2.65 \times 5 \times 10^{-3} \text{ \Omega}$
$\text{R} = 13.25 \times 10^{-3} \text{ \Omega}$ ($\frac{1}{2}$)