Circuit Fundamentals

Resistors in parallel. Current divider circuit and equation

Resistors in parallel. Current divider

Two or more resistors are said to be in parallel, if identical voltage is across all the resistors.

Resistor in parallel

In accordance to Kirhhoff’s Law the current IS=I1+I2+...+IN, and V1=V2=...=VN=V.

Here I1=VR1, I2=VR2, ...IN=VRN. So IS=V(1R1+1R2+...1RN)=VReq.

Here parallel resistors can be replaced by the equivalent resistance 1Req=1R1+1R2+...1RN, and Req=11R1+1R2+...1RN.

Resistors in parallel and current divider

Then current through a resistor in parallel circuit is In=1Rn1R1+1R2+...1RNIS. This equation is called current divider. Current divider is a linear circuit, producing output current equal to a fraction of the input current.

For example, if R1=1Ohm, R2=2 Ohm, R3=4 Ohm, R4=2Ohm and Is=4A, then I3=49A.