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1 answer:
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a) Increase
b) Unchanged
c) Increase
Explanation:
a)
The charge on a capacitor charging in a RC circuit connected to a battery follows the exponential equation:
where
is the final charge stored in the capacitor, where C is the capacitance and V is the voltage of the battery
t is the time
R is the resistance of the circuit
The capacitor reaches 90% of its final charge when
Substituting and re-arranging the equation, we find:
We see that if we double the RC constant, then
So the time taken will double as well:
So, the answer is "increase"
b)
In this second part, the battery voltage is doubled.
According to the equation written in part a),
this means also that the final charge stored on the capacitor will also double.
However, the equation that gives us the time needed for the capacitor to reach 90% of its full charge is
We see that this equation does not depend at all on the voltage of the battery.
Therefore, if the battery voltage is doubled, the final charge on the capacitor will double as well, but the time needed for the capacitor to reach 90% of its charge will not change.
So the correct answer is
"unchanged"
c)
In this case, a second resistor is added in series with the original resistor of the circuit.
We know that for two resistors in series, the total resistance of the circuit is given by the sum of the individual resistances:
Since each resistance is a positive value, this means that as we add new resistors, the total resistance of the circuit increases.
Therefore in this problem, if we add a resistor in series to the original circuit, this means that the total resistance of the circuit will increase.
The time taken for the capacitor to reach 90% of its final charge is still
As we can see, this time is directly proportional to the resistance of the circuit, R: therefore, if we add a resistor in series, the resistance of the circuit will increase, and therefore this time will increase as well.
So the correct answer is
"increase"
Answer:
At the point of dropping the object, by Newton's first law due to gravitational force = m × g, accelerates
By Newton's Second law the object reaches impacts on the air with the gravitational force resulting in changing momentum of m×(Final Velocity - Initial Velocity)
As the velocity increases, the rate of change of momentum becomes equivalent to the gravitational force and by Newton's third law, the action action and reaction are equal and opposite hence they cancel each other out
The body then moves at a constant uniform motion down according to Newton's first law
Explanation:
At the point the object of mass, m, is dropped from the height of the tower, the only force acting on the object is the gravitational force such that the object has an acceleration which is the acceleration due to gravity, g, and the gravitational force is therefore = m × g
As the speed of the object increases while the object is falling with the gravitational acceleration the rate at which the object cuts through layers of air which (by Newton's first law of motion, are at rest ) has some buoyancy effect also increases therefore, the object is constantly increasingly changing the momentum of the air which by Newton's second law results, at an high enough velocity, and by Newton's third law, in a force equal to the applied gravitational force
Therefore, the force of the air drag becomes equal to the gravitational force, cancelling each other out and the object then moves according to Newton;s first law, in uniform motion of a constant speed while still falling down.