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JEE Main 2013 (9 Apr, Shift 1) · Mutual Inductance

Mutual Inductance question from JEE Main 2013 (9 Apr, Shift 1)

Q59JEE Main 2013 · 9 APR · SHIFT 1Medium

Mutual Inductance

Two coils, X and Y, are kept in close vicinity of each other. When a varying current, I(t)I(t), flows through coil X, the induced emf (V(t))(V(t)) in coil Y, varies in the manner shown here. The variation of I(t)I(t), with time, can then be represented by the graph labelled as graph:

Figure

Figure

(A)

Figure

(B)

Figure

(C)

Figure

(D)

Show answer and solution

Answer: (b)

I(t)tV>0V<0V=0
  1. V=−MdIdtV = -M\dfrac{dI}{dt}, so the slope of I(t)I(t) is opposite in sign to VV and proportional to it.
  2. First part: V>0V > 0, starting and ending at zero, so II falls with zero slope at both ends (a smooth cosine-like fall).
  3. Second part: VV is a negative constant, so II rises linearly.
  4. After that V=0V = 0, so II stays constant. Only graph C has this shape.
  5. So the answer is (b) C.
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