Voltage and Current Dividers

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Voltage Division

When we have a voltage across a string of resistors connected in series, we can express the voltage across a single resistor as a ratio of voltages and resistances, without ever knowing the current.

File:Voltage division1.jpg

In the circuit above,

or

We can generalize this equation for number of resistors in series with the equation:

where is the voltage across resistor </math>k is the voltage across the whole string of resistors.

Current Division

When we have a current flowing through resistors in parallel, we can express the current flowing through a single resistor as ratio of currents and resistances, without ever knowing the voltage.

File:Current division1.jpg

In the circuit above

or

where is the current flowing through all the resistors. Note that the numerator on the right is R2, not R1. Remember that a larger resistance will carry a smaller current.

We can generalize the equation for number of resistors in parallel with the equation:

where is the current flowing through resistor and is the current flowing through all the resistors.

Practice Problems

Problem 1

Use voltage division to find in the circuit below:

File:Voltage division problem1.jpg

click here for the solution

Problem 2

Simplify the circuit and then use current division to find in the circuit below:

File:Current division problem1.jpg

click here for the solution