# Voltage and Current Dividers

## Contents |

## Voltage Division

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

In the circuit above,

or

We can generalize this equation for *N* resistors in series with the equation:

where *v*_{k} is the voltage across resistor *k* and *v* is the voltage across the whole string of resistors.

## Current Division

Resistors in parallel divide up the current. 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.

In the circuit above

or

where *i* 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 *N* resistors in parallel with the equation:

where *i*_{k} is the current flowing through resistor *k* and *i* is the current flowing through all the resistors.

## Practice Problems

### Problem 1

Use voltage division to find *v*_{x} in the circuit below:

### Problem 2

Simplify the circuit and then use current division to find *i*_{x} in the circuit below: