DIVIDER CIRCUITS & KCF LAW || Lessons In Electric Circuits -- Volume I (DC) Chapter 6

DIVIDER CIRCUITS AND KIRCHHOFF'S LAWS

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Voltage divider circuits

Let's analyze a simple series circuit, determining the voltage drops across individual resistors:





From the given values of individual resistances, we can determine a total circuit resistance, knowing that resistances add in series:

From here, we can use Ohm's Law (I=E/R) to determine the total current, which we know will be the same as each resistor current, currents being equal in all parts of a series circuit:

Now, knowing that the circuit current is 2 mA, we can use Ohm's Law (E=IR) to calculate voltage across each resistor:

It should be apparent that the voltage drop across each resistor is proportional to its resistance, given that the current is the same through all resistors. Notice how the voltage across R₂ is double that of the voltage across R₁, just as the resistance of R₂ is double that of R₁.
If we were to change the total voltage, we would find this proportionality of voltage drops remains constant:

The voltage across R₂ is still exactly twice that of R₁'s drop, despite the fact that the source voltage has changed. The proportionality of voltage drops (ratio of one to another) is strictly a function of resistance values...............................................