Voltage Calculation for Nichrome Wire

What is the voltage across a 1.0-meter nichrome wire with a radius of 0.50 mm carrying a current of 0.50 amperes?

a) 0.25 volts

b) 1.0 volts

c) 2.0 volts

d) 4.0 volts

Answer:

The voltage across a 1.0-meter nichrome wire with a radius of 0.50 mm carrying a current of 0.50 amperes is calculated to be approximately 0.635 volts, which doesn't match any of the provided options.

To find the voltage, we need to calculate the electrical resistance first, which can be done with the formula R = ρl/A where R is resistance, ρ is resistivity, l is the length of the wire, and A is the cross-sectional area of the wire. For a wire of circular cross-section, A = πr^2 where r is the radius.

Calculate A first: A = π*(0.0005 m)^2 = 7.85 x 10^-7 m².

Then find R: R = ρl/A = 1.0 × 10^-6 Ωm * 1m / 7.85 x 10^-7 m² = 1.27 Ohms.

Now we find the voltage using Ohm's law, V = IR, where I is the current and V is the voltage across the wire's ends. Plug the given current and calculated resistance into the formula to find V = (0.50 A) * (1.27 Ω) = 0.635 volts. None of the provided options in the question matches this result.

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