Voltage is the speed of electricity

Accelerating voltage

Subject matter

Electric voltage, electric charge. Elemental charge. Kinetic energy.

learning goals


Electrons emerge from a hot cathode (negative pole) and move to the anode (positive pole). In doing so, they are attracted to the anode; the electrons are accelerated.

Calculate how the final velocity of the electrons depends on the voltage U, the elementary charge e = 1.6 · 10-19 C and the electron mass m = 10-30 depend on kg! Justify the following reshaping steps and check by clicking on the "Tip"!

From the voltage U = W / e we calculate the increase in kinetic energy:

E.kin = e U (tip)

m · v2 / 2 = e * U

v2 = 2 e rev / m (tip)

Result: v = √ (2 e U / m)

Calculate the velocity v that electrons get after passing through a certain accelerating voltage with the following form!

Note: The above formula only applies to "classical conditions" - the speed of the electrons must be well below the speed of light c0 = 3 · 108 m / s = 300 x 106 m / s lie (classical approximation).
Compare your results with c0! Up to which acceleration voltage does it make sense to calculate "conventionally"?


Where are "individual electrons" accelerated in technical devices? Research applications from research and technology!

  • Calculate the final speed of the accelerated electrons for different voltages (eg: U = 350 V, U = 5 kV, U = 8 kV, U = 20 kV)!
  • Does twice the acceleration voltage lead to twice the speed of the electrons?
  • Compare the final speed of electrons with the speeds of heavier particles that are accelerated at the same voltage! For example, what can you do for protons (m = 10-27 kg) testify?
  • When fast electrons hit an obstacle, X-rays are generated. Research the acceleration voltages from which X-rays can occur!
  • At high speeds, relativistic effects must be taken into account (cf. 20 Relativity). Research the connections in this "non-classical case"!