Voltage divider method

In this lesson, we will learn:

• A review on Ohm’s Law and how to manipulate the equation (V=IR) to solve for voltage, current, and resistance.
• How to solve problems for voltage and resistance with a shortcut equivalent of Ohm’s Law; the Voltage Divider Method general formula we will be using is:
• What is the relationship between voltage, current, and resistance?
• $V_{x} = V_{total} \, \cdot \, \frac{R_{x}} {R_{total}}$
• When and how to use the Voltage Divider Method to skip to solving questions for voltage and/or resistance without having to first solve for current.
• How we can use the Voltage Divider Method to supplement Ohm’s Law to help us in this chapter

• The Voltage Divider Method is a formula we can utilize as a shortcut to Ohm’s Law $(V=IR)$ in certain cases—when the electric circuit question is asking for voltage and/or resistance, it is no longer necessary to solve for the electric current before calculating the voltage across center resistors.


• The general formula for the Voltage Divider Method is as follows:
• $V_{x} = V_{total} \, \cdot \, \frac{R_{x}} {R_{total}}$


• Where:
• $V_{x}$ is the voltage drop across a particular resistor $x$
• $V_{total}$ is the total voltage of the circuit supplied by the battery/source
• $R_{x}$ is the resistance of a particular resistor $x$
• $R_{total}$ is the total, combined sum of resistances of the circuit


• In some cases, we will want to apply the voltage divider to only a section of the circuit (i.e. the parallel component only)—not to the entire circuit
• In those cases, the total voltage will reflect the voltage amount of that portion only (i.e. the equivalent parallel resistance; $V_{parallel}$)
• And, the total resistance will reflect the sum of resistances of that portion only (i.e. $R_{parallel}$)
• In other words, you would replace the variables with “total” subscripts with the portion amount only (i.e. $V_{total}$ = $V_{parallel}$ and $R_{total}$ = $R_{parallel}$)


• If the question provides the current $I$ as a given, it usually hints that one or more parts of the question will not require the voltage divider (since the voltage divider formula does not include current)
• If the question asks to solve for the current, it will require Ohm’s Law ($V=IR$) and can be supplemented by the voltage divider method depending on the question