I read a few places that some circuits may have low voltage applied to them but a high current running through them and vice versa. How is this possible? Since the current is induced by the voltage would a low voltage not mean a low current?

Obviously a circuit with a low resistance would give higher current than one with a high resistance at the same voltage. Is that what they mean?

 

Yes. The three things are related: voltage, current, and load resistance. All combinations of voltage and current are possible. Some are dangerous and some are not. 6 mA is the most current you want traveling through your heart. It will stop it!

 

I read that to reduce energy loss the electricity companies transmit energy with a high voltage but low current. How is this possible?

A high voltage will create a high current and if you increase the resistance that will increase the energy loss. How do they use high voltages but low currents and decrease the energy loss through friction by doing so?

 

this done with the help of transformers.
lets go a little into how and why.
a turbine generates mechanical power by rotaing action given to it by say gas or steam.
this power is connected into electrical power by generators.
this power is given by power = voltage*current (simply put)
transformer is constant power device it does not add to power and has negligible losses. whatever load(electrical) u apply on generator will apply a opposing torque on turbine hence power can not increase beyond max capacity.
as power is constant we step up voltage on secondary ised of transformer so current decreases.
power=VI=constant.
therefore
V(1)I(1)=V(2)I(2)

now since current on secondary (max current for that given voltage) has been stepped down the power losses due to resistance in wires (R) will reduce
as I^2.R is power loss we reduce the power loss by the square of the factor
we step down the current. stepping it lower will be better.

 

6 mA is the most current you want traveling through your heart. It will stop it!

But it has to get there first.

 

ohms law: V=IR and powerL P=IsquaredR [how do you put on superscript?]

electricity companies use higher voltage because as the others have said you need less voltage to achieve the same power as that of a lower voltage and high current. This is possible through transformers. A step down transformer is used at the other end to "step down" the voltage which from the circuit's point of view is a high impedance which doesnt allow the current to get to high according to V=IR. The benefit of this approach is because there is less current flowing through the circuit, the circuit's power conduits will draw less power. This concept is easy to understand when you look at the power formula. As the resistance of wire is generally fixed (not taking into account factors like temperature) the only other factor in the power formula is current. so as the current increases, the power dissipation through that section of wire will increase logarithmically. Its much more efficient to run the circuit at the higher voltage but much more dangerous, which is why the power lines are suspended so high above ground.This strategy constitutes a saving in energy. In this case a massive saving making long distance power distribution possible.
I hope that my own understanding of this is not erroneous.
Please refer to the following:
http://www.allaboutcircuits.com/vol_2/chpt_9/2.html

 

An example of "low" voltage and "high" current can be found in welding equipment.

Another example can be found in high-amperage DC power supplies for internet nodes and telecommunications points-of-presence - typically 48 Volts at 120 Amps or more. Very dangerous! That much current can make a screwdriver or belt-buckle explode, causing severe burns, blindness, or death. Most electricians are far more comfortable around 480Vac than 48Vdc!