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Magazine Chapter 30: Q57P (page 900)
In Figure,the ideal battery has , and the fuse in the upper branch is an ideal3.0 A fuse. It has zero resistance as long as the current through it remains less than3.0 A . If the current reaches3.0 A , the fuse 鈥渂lows鈥� and thereafter has infinite resistance. Switch S is closed at timet = 0 . (a) When does the fuse blow? (Hint: Equation 30-41 does not apply. Rethink Eq. 30-39.) (b) Sketch a graph of the current i through the inductor as a function of time. Mark the time at which the fuse blows.
Short Answer
a) Time at which the fuse blows is t = 1.5 s
b) The sketch of graph of the current through the inductor as a function of time and the time at which fuse blows is given below.
Step by step solution
Given
i) Resistance is
ii) Inductance is
iii) Battery emf is
iv) Current through the fuse is
Understanding the concept
We use the concept of loop rule for the give circuit. Applying the loop rule, we can find the time at which the fuse blows. We can sketch the graph of the current through the inductor as a function of time.
Formulae:
For the given loop,
(a) Calculate the time at which the fuse blows.
Time at which the fuse blows:
We can apply the loop rule.
Before the fuse blows, the current through the resistor is zero, so we can write
role="math" localid="1661427781225"
Integrating on both sides, we get
Plugging the values, we get
(b) Sketch the graph of the current through the inductor as a function of time and mark the time at which the fuse blows:
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