<span>A motor produces less mechanical energy than the energy it uses because the motor looses some energy to heat.</span>
Answer:
The fraction fraction of the final energy is stored in an initially uncharged capacitor after it has been charging for 3.0 time constants is

Explanation:
From the question we are told that
The time constant 
The potential across the capacitor can be mathematically represented as

Where
is the voltage of the capacitor when it is fully charged
So at


Generally energy stored in a capacitor is mathematically represented as

In this equation the energy stored is directly proportional to the the square of the potential across the capacitor
Now since capacitance is constant at
The energy stored can be evaluated at as


Hence the fraction of the energy stored in an initially uncharged capacitor is

Humans can not see any of the above with their eyes
Resistance ∞ (proportional) length
resistance ∞ 1/ area
therefore,
(the constant that we take is known as the resistivity)
resistance = (resistivity*length )/ area
resistivity = (resistance * area ) / length
= (3 * 45) / 3 = 135/3 = 45 Ωm
in short your answer is 45 Ωm
Answer:
(a) 
(b) neither increasing or decreasing
(c) opposite to the flow of charge carriers
Explanation:
The current through an inductor of inductance L is given by:
(1)
(a) The induced emf is given by the following formula
(2)
You derivative the expression (1) in the expression (2):

(b) At t=0 the current is zero
(c) At t = 0 the emf is:

w, L and Imax have positive values, then the emf is negative. Hence, the induced emf is opposite to the flow of the charge carriers.
(d) read the text carefully