Answer:
a) R₁ = 14.1 Ω, b) R₂ = 19.9 Ω
Explanation:
For this exercise we must use ohm's law remembering that in a series circuit the equivalent resistance is the sum of the resistances
all resistors connected
V = i (R₁ + R₂)
with R₁ connected
V = (i + 0.5) R₁
with R₂ connected
V = (i + 0.25) R₂
We have a system of three equations with three unknowns for which we can solve it
We substitute the last two equations in the first
V = i (
)
1 = i (
)
1 = i (
) =
i² + 0.75 i + 0.125 = 2i² + 0.75 i
i² - 0.125 = 0
i = √0.125
i = 0.35355 A
with the second equation we look for R1
R₁ =
R₁ = 12 /( 0.35355 +0.5)
R₁ = 14.1 Ω
with the third equation we look for R2
R₂ =
R₂ =
R₂ = 19.9 Ω
Part a
The average speed = total distance traveled upon total time taken.
we know, distance =speed × time
Average speed = 
insert the values:


=
km/hr
= 46.43 km/hr
Hence, the average speed for the trip is 46.43 km/hr.
Part b
the total distance between two cities via this route would be the average speed times the total time taken = 46.43 km/hr × 2.9 hr = 134.65 km
(because 175 minutes = 2.9 hours)
Hence, the total distance between two cities via this route is 134.65 km.
Answer:
The charged particle follows a spiral path in a magnetic field.
Explanation:
A charge immersed in a region with an electric field experiences a force that acts along the same direction of the electric field. In particular:
- The force has the same direction as the electric field if the charge is positive
- The force has the opposite direction as the electric field if the charge is negative
Therefore, a charge moving in an electric field is accelerated along the direction of the electric field.
On the other hand, a charge in motion in a region with a magnetic field experiences a force that acts perpendicular to the direction of the field. This means that a charge in motion in a magnetic field will acquire a circular motion in the plane perpendicular to the direction of the magnetic field.
As a result, if the particle has also a original motion outside this plane, its final motion will consist of:
- A uniform motion along that direction, +
- A circular motion along the plane perpendicular to the field
So, the resultant motion of the particle will be a spiral path. So the correct answer is
The charged particle follows a spiral path in a magnetic field.