DC electricity

• Internal resistance


  Internal resistance, in Ohms (Ω), is the resistance inside a battery. In a circuit diagram, we draw a battery in series with its internal resistance (r).

  
  

   ε =  electro-motive force (EMF) = ideal/max voltage of a battery with no internal resistance.

  
  

  V is slightly less than ε, because the internal resistance steals a bit of energy from the electrons

  
  

  Equation: V = ε − Vr Vr = ε − Ir, I is total current of circuit(current going through internal resistance, Ir is voltage across internal resistance.

  
• Kirchhoff's current Law


  Says that the current going into a junction must be the same as the current coming out of that junction.

  
  

  Equation: I(in) = I(out)

  Total current: I = I1 + I2

  
• Kirchhoff's voltage law


  The sum of all voltages around a closed loop must

  always add up to be 0.

  For this loop: V(AB) + V(BC) + V(CD) + V(DA) = 0

  Voltage can be positive or negative. Positive voltages are those which add energy to electrons and negative voltages are those which take energy away. Batteries +, light bulb -.

  Often change V to IxR: I(a)R(a) + I(b)R(b) + V(b)+ I(c)R(c)+ V(a)= 0

  
• Rules to follow for Kirchhoff's voltage law

  • Choose loop.
  • Choose a direction to go around loop.
  • Figure out the direction of current in each branch of loop
  • Based on the direction of the current and the direction to go around loop in, figure out whether each voltage is positive or negative. If electrons enter with more energy than they leave with then the voltage is positive.
  • Add up all the voltages, and replace V's with IR's