Resistance of a metal wire of length $1\, m$ is $26\, \Omega$ at $20^{\circ} C$. If the diameter of the wire is $0.3\, mm ,$ what will be the resistivity of the metal at that temperature ?
Resistance of a metal wire of length $1\, m$ is $26\, \Omega$ at $20^{\circ} C$. If the diameter of the wire is $0.3\, mm ,$ what will be the resistivity of the metal at that temperature ?
Given $R =26 \Omega$
$D =0.3 mm =3 \times 10^{-4} m$
$L =1 m$
Using the expression
$R=\frac{\rho L}{A} \quad$ or $\quad \rho=\frac{R A}{L}=\frac{R \pi D^{2}}{4 L}$
Or $\rho=\frac{26 \times 3.14 \times\left(3 \times 10^{-4}\right)^{2}}{4 \times 1}$
$=1.84 \times 10^{-6} \Omega m$
This material is manganese.
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The electrical resistivity of few materials is given below in ohm-metre. Which of these materials can be used for making element of a heating device ?
$A$
$6.84 \times 10^{-8}\, \Omega m$
$B$
$1.60 \times 10^{-8}\, \Omega m$
$C$
$1.00 \times 10^{-4}\, \Omega m$
$D$
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The electrical resistivity of few materials is given below in ohm-metre. Which of these materials can be used for making element of a heating device ?
| $A$ | $6.84 \times 10^{-8}\, \Omega m$ |
| $B$ | $1.60 \times 10^{-8}\, \Omega m$ |
| $C$ | $1.00 \times 10^{-4}\, \Omega m$ |
| $D$ | $2.50 \times 10^{12}\, \Omega m$ |
| $E$ | $4.40 \times 10^{-5}\, \Omega m$ |
| $F$ | $2.30 \times 10^{17}\, \Omega m$ |
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Two wires $A$ and $B$ are of same metal, have the same area of cross$-$section and have their lengths in the ratio $2: 1$. What will be the ratio of currents flowing through them respectively, when the same potential difference is applied across length of each of them ?
Two wires $A$ and $B$ are of same metal, have the same area of cross$-$section and have their lengths in the ratio $2: 1$. What will be the ratio of currents flowing through them respectively, when the same potential difference is applied across length of each of them ?