An electric motor is plugged into a standard wall socket and is running at normal speed. Suddenly, some dirt prevents the shaft of the motor from turning quite so rapidly. What happens to the back emf of the motor, and what happens to the current that the motor draws from the wall socket?

a.) The back emf decreases, and the current drawn from the socket decreases.
b.) The back emf increases, and the current drawn from the socket decreases.
c.) The back emf decreases, and the current drawn from the socket increases.
d.) The back emf increases, and the current drawn from the socket increases.

Option C is correct answer.

Explanation:

The EMF() produced by a coil is given by

Here, is number of turns , is area is Magnetic field and is rate at which coil turns.

If dirt prevents the shaft from turning that means is decreasing (As rate is decreasing). That simply means Induced EMF decreases.

But according to formula of Self Inductance

( Here is self inductance and is rate of change of current).

We can say that the EMF is depends as negative of rate of current growth.

So, from this formula we can say that the EMF is decreases and the current drawn from the socket increases.

The correct option is C.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .