Now let us assume the electrophoresis is being taken place in liquid medium. What happens when voltage is removed? All molecules are diffused and mixed up again and electrophorectic mobility is not detectable soon after voltage was removed. If we want to see the position of molecule after electrophoresis, we need to minimize the diffusion. For this purpose, solid matrix is required in the process of electrophoresis. Polyacrylamide is commonly used matrix is protein electrophoresis while polymerized agarose is used for DNA electrophoresis.
Electrophoresis at constant current or constant voltage?
Ohm's law relates V to current, I by electrical resistance, R as follow

We might think that increasing V would result in increase in current which in turn give faster electrophoretic mobility and doing experiment at fixed high voltage is better (??). However, large current results in sufficient power generation (watts law). The power generated during electrophoresis is given by
W = I2 R
Heat generation is not desirable in electrophoresis as this result in bad resolution of separation due to convection of buffer causing mixing of separated molecule. Moreover, temperature (heat) decreases viscosity of buffer. Decrease in viscosity results in easier movement of ions resulting in decrease in resistance. According to Ohm's law decrease in resistance at fixed voltage result in further increase in current and head generation. Additionally, at high temperature thermolabile molecule like protein may breakdown during electrophoresis and may not be separated in native form. Thus, except specify applications, constant current may be a better option.
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