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Science · 2026 · 2 marks
CBSE 2026 · Region 1 · Set 1 · Q34
The resistance of a wire of $\displaystyle 0.01$ cm radius and $\displaystyle 1.0$ cm length is $\displaystyle 7 \Omega$. Calculate its resistivity.An electric heater is rated $\displaystyle 220$ V; $\displaystyle 11$ A. Calculate the power consumed if the heater is operated at $\displaystyle 200$ V.
The resistance of a wire of $\displaystyle 0.01$ cm radius and $\displaystyle 1.0$ cm length is $\displaystyle 7 \Omega$. Calculate its resistivity.
An electric heater is rated $\displaystyle 220$ V; $\displaystyle 11$ A. Calculate the power consumed if the heater is operated at $\displaystyle 200$ V.
Marking-scheme solution
(a)
\(\displaystyle \mathrm{r}=0.01 \mathrm{~cm}=1 \times 10^{-4} \mathrm{~m}\)
\[\begin{aligned}
& l=1 \mathrm{~cm} \\
& \mathrm{R}=\rho \frac{l}{\mathrm{~A}}
\end{aligned}
\]
\[\rho=\frac{\mathrm{RA}}{l}=\frac{R \times \pi r^{2}}{l}
\]
\[\rho=\frac{7 \times 22 \times 10^{-8}}{7 \times 0.01}
\]
\[\rho=22 \times 10^{-8} \times 10^{2}
\]
\[\rho=22 \times 10^{-6} \Omega \mathrm{~m}=2.2 \times 10^{-5} \Omega \mathrm{~m}
\]
(b)
Resistance of electric heater \(\displaystyle \mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}\)
\[\mathrm{R}=\frac{220}{11}
\]
\[R=20 \Omega
\]
\[P=\frac{V^{2}}{R}
\]
\[\mathrm{P}=\frac{200 \times 200}{20}
\]
\[\text { P = 2000W/ } 2 \text { kW }
\]
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