We encounter divider circuits frequently in circuit analysis.
Voltage divider
For the above circuit (a voltage divider), we have:
We may occasionally see voltage dividers in circuits with op amps: As always, our constraints are that , that , and that . It follows from Kirchhoff’s laws that:
equating for :
and this holds for other funky looking resistor combinations.
Current divider
For the above circuit (a current divider), we have:
Phasor analysis
For impedances in series:
which is the equivalent of DC voltage division.
For impedances in parallel, we have: