(i) Definition of 1 Volt:
The potential difference between two points is said to be 1 volt when 1 joule of work is done in moving a charge of 1 coulomb from one point to the other.
$$1 \text{ V} = \frac{1 \text{ J}}{1 \text{ C}}$$
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(ii) Finding the length of the wire:
Given: diameter $d = 0.2 \text{ mm} = 2 \times 10^{-4}$ m, $\rho = 1.6 \times 10^{-8}$ Ω m, $R = 14$ Ω
Area of cross-section:
$$A = \frac{\pi d^2}{4} = \frac{\pi \times (2 \times 10^{-4})^2}{4} = \pi \times 10^{-8} \text{ m}^2$$
Using $R = \rho \dfrac{l}{A}$:
$$l = \frac{RA}{\rho} = \frac{14 \times \pi \times 10^{-8}}{1.6 \times 10^{-8}} = \frac{14\pi}{1.6} \approx 27.5 \text{ m}$$
Effect of doubling the diameter:
If diameter is doubled, area becomes $4A$. Since $R \propto \dfrac{1}{A}$, resistance becomes $\dfrac{14}{4} = 3.5$ Ω.
Resistance decreases by 10.5 Ω (from 14 Ω to 3.5 Ω).
Source: Chapter 11 – Electricity, Section 11.4 & 11.5
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