The power dissipated across a wire of length 0.5 m and area of cross-section $0.2 imes 10^{-6}\, ext{m}^2$ is 10 W when a steady current flows through it. Calculate the following quantities :
(Given : resistivity of the material of the wire is $1 imes 10^{-6}\,\Omega ext{m}

Question

The power dissipated across a wire of length 0.5 m and area of cross-section $0.2 	imes 10^{-6}\,	ext{m}^2$ is 10 W when a steady current flows through it. Calculate the following quantities :
(Given : resistivity of the material of the wire is $1 	imes 10^{-6}\,\Omega	ext{m}$)
i) Resistance of the wire ;
ii) The current flowing through the wire ;
iii) The current density for the wire.

Accepted Answer

> [!TLDR]
> From $R=ho l/A$ get $R=2.5\,\Omega$; from $P=I^2R$ get $I=2\,	ext{A}$; then $J=I/A=1	imes10^{7}\,	ext{A m}^{-2}$.

**Given**

Length $l=0.5\ 	ext{m}$, area $A=0.2	imes10^{-6}\ 	ext{m}^2$, power $P=10\ 	ext{W}$, resistivity $ho=1	imes10^{-6}\ \Omega	ext{m}$.

**(i) Resistance of the wire**
$$R=\frac{ho l}{A}=\frac{(1	imes10^{-6})(0.5)}{0.2	imes10^{-6}}=\frac{0.5	imes10^{-6}}{0.2	imes10^{-6}}=2.5\ \Omega$$

**(ii) Current through the wire**

From $P=I^2R$: …

Q.The power dissipated across a wire of length 0.5 m and area of cross-section $0.2 \times 10^{-6}\,\text{m}^2$ is 10 W when a steady current flows through it. Calculate the following quantities :
(Given : resistivity of the material of the wire is $1 \times 10^{-6}\,\Omega\text{m}$ )

Concept understanding — Resistivity

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