A copper wire having cross- sectional area of `0.5 mm^2` and a length of ` 0.1 m` is initially at `25^@C` and is thermally insulated form the surrounding. If a current of `10A` is set up in this wire, (a) find the time in which the wire will start melting. (b) What will be the change of resistance with time, if the length of the wire is doubled? For copper, resistivity is `1.6xx10^(-8)Omega m,` density is `9,000 kgm^(-3)` and specific heat capacity is `0.09 cal g^(-1)C^(-1).` Melting temperature of copper is `1075^@C`

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as required.

### Part (a): Finding the time in which the wire will start melting

1. **Identify the known values**:
- Cross-sectional area (A) = 0.5 mm² = \(0.5 \times 10^{-6} \, m^2\)
- Length (L) = 0.1 m
- Initial temperature (T_initial) = 25 °C
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