Step 1: Understanding Air Permeability: Air permeability is the ability of a fabric to allow air to pass through it. It's a crucial factor for comfort, especially in clothing.
Step 2: Understanding Twist Factor: Twist factor is a measure of the amount of twist in a yarn. Higher twist factor means a tighter, more compact yarn.
Step 3: Relationship Between Twist and Air Permeability: As the twist factor increases (up to a certain point), the yarn becomes more open and porous, allowing air to flow through easily. But after reaching a certain level, increase in twist makes the yarn compact, thus reducing the air permeability. Thus the relationship is not exactly linear.
Step 4: Analyzing the Options:
(a) The air space in the yarn is reduced: This is incorrect as increase in twist factor increases the air space.
(b) The warp and weft cover factor is high: This is not directly connected to the air permeability of yarn.
(c)The air space in the yarn is high: This is correct as higher twist factor makes the yarn more open.
(d) The warp and weft cover factor is constant: This option has no direct relation with the twist factor.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.