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X and Y are two metallic coils arranged in such a way that when the steady change in current flowing in coil X is 4 A, the change in magnetic flux associated with coil Y is 0.4 Wb. The mutual inductance of the system of these coils is …….. H.

Asked in GUJCET 2008 · Mutual inductance and induced EMF

• (1) 0.8
• (2) 0.1
• (3) 0.2
• (4) 5

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 0.8 H from these data — even multiplying gives 0.4×4 = 1.6. Sanity check: M = (0.4)/4 = 0.1 H; 0.8 H would need a current change of only 0.5 A.
• (3) 0.2 H is (0.4)/2, which would fit a current change of 2 A, not the 4 A given here. Dividing by the actual 4 A gives 0.1 H.
• (4) No single slip gives 5: even the inverted ratio (Δ I)/(ΔΦ) is 4/(0.4) = 10. M is flux per unit current, (0.4)/4 = 0.1 H.

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