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Chapter 4: Q73PP (page 1019)

If a small part of this magnet loses its superconducting properties and the resistance of the magnet wire suddenly rises from 0 to a constant 0.005鈩�, how much time will it take for thecurrent to decrease to half of its initial value?

(a) 4.7 min ; (b) 10 min ; (c) 15 min ; (d) 30 min

Short Answer

Expert verified

It takes 10 min for the current to decrease to half of its initial value

Step by step solution

01

Current in a R-L Circuit

Current in the R-L Cirucit is given byi=蔚R1-eRLt

Where the emf of the battery is R is the resistance and L is the inductance.

02

Application

We can solve the equation for time t and we get

t=-LRlnii0

where i arei0 the current at time t and initial current respectively.

For half the current we geti=0.5i0

Hence,

t=4.4Hz0.005惟ln0.5i0i0t=609.9s鈮�10min

Hence it takes 10 mins for the current to drop to half the value.

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