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, find the time in which the wire will start melting. For copper, resistivity is `1.6xx10^(-8)Omega m`, density is `9,000 kgm^(-3)` and specific heat capacity is `0.09 cal g^(-10)C^(-1).` Melting temperature fo copper is `1075^@C`

Explanation

To solve the problem, we need to find the time it takes for a copper wire to reach its melting point when a current is passed through it. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Cross-sectional area, \( A = 0.5 \, \text{mm}^2 = 0.5 \times 10^{-6} \, \text{m}^2 \)
- Length of the wire, \( L = 0.1 \, \text{m} \)
- Initial temperature, \( T_1 = 25 \, \text{°C} \)
- Final temperature (melting point), \( T_2 = 1075 \, \text{°C} \)
- Current, \( I = 10 \, \text{A} \)
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