The resistance of a coil is 4.2 Ω at 1000C  and the temperature coefficient of resistance of its material is 0.0040C .  Its resistance at 00C  is

# The resistance of a coil is $4.2\text{\hspace{0.17em}}\mathrm{\Omega }$ at ${100}^{0}\mathrm{C}$  and the temperature coefficient of resistance of its material is $0{.004}^{0}\mathrm{C}$ .  Its resistance at ${0}^{0}\mathrm{C}$  is

1. A

$6.5\text{\hspace{0.17em}}\mathrm{\Omega }$

2. B

$5\text{\hspace{0.17em}}\mathrm{\Omega }$

3. C

$3\text{\hspace{0.17em}}\mathrm{\Omega }$

4. D

$2.5\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{\Omega }$

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### Solution:

Resistance ${R}_{2}=4.2\mathrm{\Omega }$ Temperature ${t}_{2}={100}^{\circ }\mathrm{c}$ Temperature ${\mathrm{t}}_{1}={0}^{\circ }\mathrm{c}$
Temperature of coefficient  $\mathrm{\alpha }=0{.004}^{0}\mathrm{C}$
$\alpha =\frac{{R}_{2}-{R}_{1}}{{R}_{1}\left({t}_{2}-{t}_{1}\right)}⇒4×{10}^{-3}=\frac{4.2-{R}_{1}}{{R}_{1}×100}$

$⇒0.4{R}_{1}+{R}_{1}=4.2⇒1.4{R}_{1}=4.2\therefore {R}_{1}=3\mathrm{\Omega }$

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