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

Answer: Option D

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:

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

Calculate this to find $$L$$:

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