The equivalent resistance of n resistors in series is given by:
In our circuit, we have three resistors of
each, therefore the equivalent resistance of the circuit is
micrometer is used to measure the diameter of a thin wire
Answer:
E/4
Explanation:
The formula for electric field of a very large (essentially infinitely large) plane of charge is given by:
E = σ/(2ε₀)
Where;
E is the electric field
σ is the surface charge density
ε₀ is the electric constant.
Formula to calculate σ is;
σ = Q/A
Where;
Q is the total charge of the sheet
A is the sheet's area.
We are told the elastic sheet is a square with a side length as d, thus ;
A = d²
So;
σ = Q/d²
Putting Q/d² for σ in the electric field equation to obtain;
E = Q/(2ε₀d²)
Now, we can see that E is inversely proportional to the square of d i.e.
E ∝ 1/d²
The electric field at P has some magnitude E. We now double the side length of the sheet to 2L while keeping the same amount of charge Q distributed over the sheet.
From the relationship of E with d, the magnitude of electric field at P will now have a quarter of its original magnitude which is;
E_new = E/4
Answer:
v = (10 i ^ + 0j ^) m / s, a = (0i ^ - 9.8 j ^) m / s²
Explanation:
This is a missile throwing exercise.
On the x axis there is no acceleration so the velocity on the x axis is constant
v₀ₓ = 10 m / s
On the y-axis velocity is affected by the acceleration of gravity, let's use the equation
v_y = 
- g t
at the highest point of the trajectory the vertical speed must be zero
v_y = 0
therefore the velocity of the body is
v = (10 i ^ + 0j ^) m / s
the acceleration is
a = (0 i ^ - g j⁾
a = (0i ^ - 9.8 j ^) m / s²
- The mechanic did 5406 Joules of work pushing the car.
That's the energy he put into the car. When he stops pushing, all the energy he put into the car is now the car's kinetic energy.
- Kinetic energy = (1/2) (mass) (speed²)
And there we have it
- The car's mass is 3,600 kg.
- Its speed is 'v' m/s .
- (1/2) (mass) (v²) = 5,406 Joules
(1/2) (3600 kg) (v²) = 5406 joules
1800 kg (v²) = 5406 joules
v² = (5406 joules) / (1800 kg)
v² = (5406/1800) (joules/kg)
= = = = = This section is just to work out the units of the answer:
- v² = (5406/1800) (Newton-meter/kg)
- v² = (5406/1800) (kg-m²/s² / kg)
= = = = =
v = √(5406/1800) m/s
<em>v = 1.733 m/s</em>
