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E.M.F and Internal Resistance

Internal resistance
  • Resistance comes from electrons colliding with atoms and losing energy.
  • In a battery, chemical energy is used to make electrons move. As they move, they collide with atoms inside the battery — so batteries must have resistance.
  • This is called internal resistance. Internal resistance is what makes batteries and cells warm up when they're used.
  • \(\varepsilon=V+\text{lost volts}\)
  • \(\varepsilon=V+Ir\) (ohms law)
  • \(\varepsilon=Ir+IR\)
  • \(\varepsilon=I(R+r)\)
  • \(V=\varepsilon-Ir\)
EMF
  • The amount of electrical energy the battery produces and transfers to each coulomb of charge is called its electromotive force or e.m.f. (e).
  • Be careful, e.m.f. isn't actually a force. It's measured in volts.

  • The potential difference (p.d.) across the load resistance (R) is the energy transferred when one coulomb of charge flows through the load resistance.
  • This potential difference is called the terminal p.d. (V).
  • If there was no internal resistance, the terminal p.d. would be the same as the e.m.f.
  • However, in real power supplies, there's always some energy lost overcoming the internal resistance.
  • The energy wasted per coulomb overcoming the internal resistance is called the lost volts (v).
Using a straight line equation for Internal Resistance
  • \(\varepsilon=V+Ir\) can be rearranged into\(V=-rI+\varepsilon\).
  • This is in the same format as \(y=mx+c\) which means we can use it in a straight line equation.
  • \(V\) is on the y-axis, \(I/A\) is on the x-axis, \(r\) is the gradient, and \(\varepsilon\) is the y-intercept.
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