Question

you're designing a superconducting cable intended to carry 11.5 kA . The cable's self-inductance is 26.2 mH . Embedded copper wire is included to handle the current in the event that superconductivity is lost, and your job is to specify the minimum resistance for the copper under the requirement that the current will drop to 5.75 kA in less than 10 s after loss of superconductivity. What resistance do you specify?

Answer 1

The minimum resistance of the copper wire can be calculated using the time constant formula for an LR circuit. By considering an exponential decay of current in relation to time, the resistance can be determined to ensure the current drops to half in less than 10 seconds after superconductivity is lost.

The minimum resistance for the copper wire is 2.62 mΩ.

Step-by-step explanation:

To specify the minimum resistance for the copper wire, we need to calculate the time constant of the circuit and use it to find the resistance.

The time constant is given by the formula τ = L/R, where L is the self-inductance and R is the resistance.

Rearranging the equation, we can solve for R:

R = L/τ.

In this case, the current drops to 5.75 kA in less than 10 s after loss of superconductivity.

Therefore, we can use this time (10 s) as the characteristic time constant (τ).

Now, substituting the given values into the equation, we get

R = (26.2 mH) / (10 s)

= 2.62 mΩ.