If you want to make the total equivalent resistance as small as possible,
then you should connect the new resistor in parallel with the original one.
When resistors are in parallel, then no matter how many of them there are
or what their individual values are, the total equivalent resistance is always
less than the smallest individual one.
For resistors in parallel . . .
(1 / total resistance) = (1/R₁) + (1/R₂) + (1/R₃) + . . . however many there are.
When there are only two resistors in parallel, you can take that formula, stretch it,
massage it, exercise it, manipulate it, and you find that
Total equivalent resistance = (product of the resistors) / (sum of the resistors) .
With 100 ohms and 25 ohms in parallel,
Total equivalent resistance = (100 x 25) / (100 + 25) = 2,500/125 = <em>20 ohms</em>.
Answer:

Explanation:
At first, the 6Li ions are accelerated by the potential difference, so their gain in kinetic energy is equal to the change in electric potential energy; so we can write:

where
is the charge of one 6Li ion
is the potential difference through which they are accelerated
is the mass of each ion
v is the final speed reached by the ions
Solving for v, we find:

After that, the ions pass into a region with a uniform magnetic field of strength

The magnetic field exerts a force perpendicular to the direction of motion of the ions, and this force is given by

In order to make the ions passing through undeflected, there should be an electric force balancing this magnetic force. The electric force is given by

where E is the strength of the electric field.
Since the two forces must be balanced,

From which we get

So the strength of the electric field must be

The velocity of the combined mass after the collision is 0.84 ms-1.
<u>Explanation:</u>
According to law of conservation of momentum, the change in momentum before collision will be equal to the change in momentum of the objects after collision in isolated system.
But as it is perfectly inelastic collision in the present case, the final momentum will be based on the product of total mass of both the object with the velocity with which the collision occurred. This form is attained from the law of conservation of momentum as shown below:
So as law of conservation of momentum,

Here
= 3 kg and
= 2 kg are the masses of objects 1 and 2,
= 1.4 m/s and
= 0 are the initial velocities of object 1 and object 2,
and
are the final velocities of the objects.
So after collision, object 1 get sticked to object 2 and move together with equal velocity
=
=
. Thus the above equation will become,

So the final velocity is

Thus,
= 0.84 ms-1.
The formula for the force of gravity has ( M₁ · M₂ / D² ) in it.
After the changes, the new force will have ( 0.5M₁ · 0.5M₂ / (0.5D)² ) .
We can separate the new numbers from the original force, like this:
( 0.5M₁ · 0.5M₂ / (0.5D)² )
= ( 0.5 · 0.5 / (0.5)² ) times ( M₁ · M₂ / D² )
The first factor boils down to ' 1 '. So, those changes would
leave the strength of the force unchanged.
That's what I think.