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(B) (i) Define electrical resistivity of a material.
(ii) How will the resistivity and resistance of a conducting wire change if the length and area of cross-section of wire both are doubled? Justify your answer.
(iii) Calculate the electric current flowing through a $$\begin{aligned}& 4 \\ & \Omega\end{aligned}$$ resistor that produces $$\begin{aligned}& 100 \\ & \text{J}\end{aligned}$$ of heat every second.
(ii) How will the resistivity and resistance of a conducting wire change if the length and area of cross-section of wire both are doubled? Justify your answer.
(iii) Calculate the electric current flowing through a $$\begin{aligned}& 4 \\ & \Omega\end{aligned}$$ resistor that produces $$\begin{aligned}& 100 \\ & \text{J}\end{aligned}$$ of heat every second.
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(i) Resistivity is the resistance offered by a wire of unit length and unit area of cross section in an electric circuit. (1 Mark)
(ii) • Resistivity of conducting wire will remain same. (½ Mark)
• Resistivity is the characteristic property of the material. (½ Mark)
• Resistance will remain same (½ Mark)
• $R = \rho \frac{l}{A}$
If $l' = 2l$, $A' = 2A$
$R' = \rho \frac{l'}{A'}$
$R' = \rho \frac{2l}{2A}$
$R' = R$ (½ Mark)
(iii) $H = I^2 R t$ (1 Mark)
$I = \sqrt{\frac{H}{Rt}}$
$I = \sqrt{\frac{100}{4 \times 1}}$ (1 Mark)
$I = 5\text{ A}$
(ii) • Resistivity of conducting wire will remain same. (½ Mark)
• Resistivity is the characteristic property of the material. (½ Mark)
• Resistance will remain same (½ Mark)
• $R = \rho \frac{l}{A}$
If $l' = 2l$, $A' = 2A$
$R' = \rho \frac{l'}{A'}$
$R' = \rho \frac{2l}{2A}$
$R' = R$ (½ Mark)
(iii) $H = I^2 R t$ (1 Mark)
$I = \sqrt{\frac{H}{Rt}}$
$I = \sqrt{\frac{100}{4 \times 1}}$ (1 Mark)
$I = 5\text{ A}$