Question

what should be the lenght of nichrome wire of resistance 4.5 ohms if the length of similar wire is 60 cm and resistance 2,5 ohms

Answer 1

What should be the length of nichrome wire of resistance 4.5 ohms if the length of similar wire is 60 cm and resistance 2,5 ohms?

The resistance of a given object depends primarily on two factors: What material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area. Also, for a given material, the resistance is proportional to the length. The resistance $R$ of a conductor of uniform cross section, therefore, can be computed as

$$R = \frac {\rho l}{A}$$

where $l$ is the length of the conductor, measured in metres [m], $A$ is the cross-section area of the conductor measured in square metres $[\mathfrak{m}^2]$, and $\rho$ (rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm-metres $(\Omega \cdot \mathfrak{m})$.

Therefore:

$$R _ {1} = \frac {\rho l _ {1}}{A}$$ $$R _ {2} = \frac {\rho l _ {2}}{A}$$

Or:

$$\frac {R _ {2}}{R _ {1}} = \frac {l _ {2}}{l _ {1}}$$

Finally:

$$l _ {2} = \frac {l _ {1} R _ {2}}{R _ {1}} = 60 \mathrm{~cm} * \frac {4.5}{2.5} = 108 \mathrm{~cm}$$

Answer: 108 cm