Time constant is defined as the time required select one: a. for the deflection to fall (decay) 57% of the peak deflection b. for the deflection to fall (decay) to 47% of the peak deflection c. for the deflection to fall (decay) to 37% of the peak deflection d. for the deflection to fall (decay) 77% of the peak deflection

c. for the deflection to fall (decay) to 37% of the peak deflection

Explanation:

For decay of deflection ( in the form of current or voltage ) to decay , the relation is as follows

i₀ is maximum current , λ is time constant ,  i is current at time t .

If t = λ

i = i₀ x .3678

This tells that time constant is the time during which current ( deflection )  decays to 36.78% of maximum current ( deflection ).

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.