Make a rule: how would you find the resistance of a parallel circuit with n identical resistors?
1 answer:
When n resistors are connected in parallel, it means they are connected to the same potential difference V:
(2)
It also means that the total current in the circuit is given by the sum of the currents flowing through each branch (each resistor) of the circuit:
(1)
By using Ohm's law:
we can rewrite (1) as
However, we said that the potential difference across each resistor is equal (eq.(2)), so we can rewrite the last formula as
From which we find an expression for the equivalent resistance of n resistors in parallel:
It also means that the total current in the circuit is given by the sum of the currents flowing through each branch (each resistor) of the circuit:
By using Ohm's law:
we can rewrite (1) as
However, we said that the potential difference across each resistor is equal (eq.(2)), so we can rewrite the last formula as
From which we find an expression for the equivalent resistance of n resistors in parallel:
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Answer:
Explanation:
We are told both planets describe a circular orbit around the star S. So, let's approach this problem begining with the angular velocity of the planet P1 with a period
:
(1)
Where:
is the velocity of planet P1
is the radius of the orbit of planet P1
Finding :
(2)
(3)
(4)
On the other hand, we know the gravitational force between the star S with mass
and the planet P1 with mass
is:
(5)
Where is the Gravitational Constant and its value is
In addition, the centripetal force exerted on the planet is:
(6)
Assuming this system is in equilibrium:
(7)
Substituting (5) and (6) in (7):
(8)
Finding :
(9)
(10)
Finally:
(11) This is the mass of the star S