A nichrome wire used as a heater coil has the resistance of 2 Ω/m. For a heater of 1 kW at 200 V, the length of wire required will be

To find the length of the nichrome wire required, you can use the formula:

$$P = \frac{{V^2}}{{R \cdot L}}$$

Where:
- $$P$$ is the power (1 kW = 1000 W)
- $$V$$ is the voltage (200 V)
- $$R$$ is the resistance per meter (2 Ω/m)
- $$L$$ is the length of the wire (which we want to find)

Let's rearrange the formula to solve for $$L$$:

$$L = \frac{{V^2}}{{P \cdot R}}$$

Now, substitute the values:

$$L = \frac{{(200\, \text{V})^2}}{{1000\, \text{W} \cdot (2\, Ω/\text{m})}}$$

Calculate this to find $$L$$:

$$L = \frac{{40000\, \text{W}}}{(2000\, Ω/\text{m})} = 20\, \text{m}$$