Question 43: Current Electricity

Question

The resistance of a wire is 5 ohm at $25^{\circ} \mathrm{C}$ and 7 ohm at $100^{\circ} \mathrm{C}$. The resistance of the wire at $0^{\circ} \mathrm{C}$ is

Accepted Answer

Let $R_0$ be the resistance at $0^\circ$C and $\alpha$ the temperature coefficient. We know
$ R(25)=R_0\bigl(1+25\alpha\bigr)=5,\quad R(100)=R_0\bigl(1+100\alpha\bigr)=7. $
From the first equation:
$    R_0 = \frac{5}{1 + 25\alpha}.    $
Substitute into the second:
$    7 = \frac{5\,(1 + 100\alpha)}{1 + 25\alpha}    \;\Longrightarrow\;     7(1 + 25\alpha) = 5 + 500\alpha    \;\Longrightarrow\;    7 + 175\alpha = 5 + 500\alpha    $
$    2 = 325\alpha    \;\Longrightarrow\;    \alpha = \frac{2}{325}.    $
Then
$    R_0 = \frac{5}{1 + 25\cdot\frac{2}{325}}          = \frac{5}{1 + \frac{50}{325}}          = \frac{5}{\frac{375}{325}}          = \frac{5\cdot325}{375}          = \frac{1625}{375}          = \frac{13}{3}\,\Omega.    $
Answer: $\displaystyle 	frac{13}{3}$ ÃÂ© (Option A).

Answer

$\frac{13}{3} \mathrm{ohm}$

Answer

$\frac{5}{3} \mathrm{ohm}$

Answer

$\frac{2}{3}$ ohm

Answer

0.1 ohm

Current Electricity

The resistance of a wire is 5 ohm at 25^{\circ} \mathrm{C} and 7 ohm at 100^{\circ} \mathrm{C}. The resistance of the wire at 0^{\circ} \mathrm{C} is

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