What does the energy hill represent on an energy diagram?
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The work done to pull the sister back on the swing is equal to the increase in potential energy of the sister:
(1)
where m is the sister's mass, g is the gravitational acceleration and
is the increase in altitude of the sister with respect to its initial position.
By calling
the angle of the chain with respect to the vertical, the increase in altitude is given by
(2)
where L is the length of the chain.
Putting (2) inside (1), we find
from which we can find the mass of the sister:
where m is the sister's mass, g is the gravitational acceleration and
By calling
where L is the length of the chain.
Putting (2) inside (1), we find
from which we can find the mass of the sister:
The equivalent resistance of several devices connected in parallel is given by
where
are the resistances of the various devices. We can see that every time we add a new device in parallel, the term 
increases, therefore the equivalent resistance of the circuit 
decreases.
But Ohm's law:
tells us that if the equivalent resistance decreases, the total current in the circuit increases. The power dissipated through the circuit (and so, the heat produced) depends on the square of the current:
therefore if there are too many devices connected in parallel, this can be a problem because there could be too much power dissipated (and too much heat) through the circuit.
where
But Ohm's law:
tells us that if the equivalent resistance decreases, the total current in the circuit increases. The power dissipated through the circuit (and so, the heat produced) depends on the square of the current:
therefore if there are too many devices connected in parallel, this can be a problem because there could be too much power dissipated (and too much heat) through the circuit.