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  1. Total resistance:
    Rtotal = Ra + Rb
    The total resistance of series resistors is the sum of individual resistances.
  2. Current in the loop:
    I = V / R = Vin / (Ra + Rb)
    According to Ohm's Law, total current equals input voltage divided by total resistance.
  3. Same current everywhere:
    In a series circuit, current is the same throughout, so the current through both Ra and Rb is I.
  4. Output voltage:
    V = I × R => Vout = I × Rb
    According to Ohm's Law, the voltage across Rb (Vout) equals current multiplied by the resistance of Rb.
  5. Substitute the current:
    Vout = (Vin / (Ra + Rb)) × Rb
    Substitute the current into the output voltage formula.
  6. Simplify the formula:
    Vout = Vin × Rb / (Ra + Rb)
    Transform to get a more intuitive voltage division formula for easier calculation.
  7. Understand the relationship:
    Vout = Vin × (Rb / (Ra + Rb))
    Output voltage equals input voltage multiplied by the ratio of Rb to total resistance.