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
A. 80 m
B. 60 m
C. 40 m
D. 20 m
Answer: Option D
Solution (By Examveda Team)
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 $$L$$:
$$L = \frac{{40000\, \text{W}}}{(2000\, Ω/\text{m})} = 20\, \text{m}$$
This Question Belongs to Electrical Engineering >> Current Electricity
The answer given is wrong. It must be 20m not 80 m. The resistance comes out to be 40 ohms. And for 40 ohms, length of the wire should be 20m.
2 ohm / m means 2 ohm for 1 meter
Similarly, 1 ohm for 0.5 meter
And, 40 ohms for 20 m.
R=V^2/P
R=40000/1000
R=40
So total length will be 40*2=80
Explination needed
£ what is meaning of this syambol