A wire of resistivity 4.40 x 10-5\(\Omega\) cm has a cross sectional area of 7.50 x 10-4 cm2. Calculate the length of the wire that will be required to make...
Question 1 Report
A wire of resistivity 4.40 x 10-5\(\Omega\) cm has a cross sectional area of 7.50 x 10-4 cm2. Calculate the length of the wire that will be required to make a 4.0\(\Omega\) resistor
Answer Details
The resistance of a wire can be calculated using the formula R = \(\frac{\rho L}{A}\), where R is the resistance, \(\rho\) is the resistivity of the wire, L is the length of the wire, and A is the cross-sectional area of the wire.
In this problem, we are given the resistivity of the wire and the cross-sectional area of the wire. We are also told that the wire needs to have a resistance of 4.0\(\Omega\). We can rearrange the formula to solve for L:
L = \(\frac{AR}{\rho}\)
Substituting the values given in the question, we have:
L = \(\frac{(7.50 \times 10^{-4} cm^{2}) (4.0 \Omega)}{4.40 \times 10^{-5} \Omega cm}\) = 68.18 cm
Therefore, the length of the wire required to make a 4.0\(\Omega\) resistor is 68.18 cm.
The correct option is: 68.18cm.
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