Circuit Fundamentals

Resistors in series. Voltage divider circuit and equation


Resistance is an electric circuit component, which is characterised by energy losses in a circuit as heat, some mechanical work, or electromagnetic radiation.

No matter how complex electric circuit is, it always can be reduced into series and parallel form.

Two or more circuit elements are in series if identical current flows through each of this elements. Series resistance are connected in chain so the same current is flowing across all resistors.

Resistors in series

Here V1=R1I, V2=R2I, ..., VN=RNI. These resistors in series can be replaced with the equivalent resistance Rseq=R1+R2+...+RN=RnN, that can replace chain of resistors in a circuit with serious connection. Here I1=I2=...=IN=I.

Voltage divider circuit

N resistors are connected in series one to the other forms voltage divider circuit. We can apply Kirhhoff’s Laws to the circuit V1=IR1, V2=IR2, ..., VN=IRN, and Vs=V1+V2+...+VN.

The voltage across every resistor as Vn=RnR1+R2+...+RNVs, here Vs is a source voltage.

This circuit is called voltage divider. Voltage divider is a linear circuit that produces output voltage equal to fraction of the input voltage. If we know all resistances in the circuit and battery voltage (or source voltage), we can find voltage drop of every resistor.

Voltage divider

For example, If R1=3 Ohm,  R2=2 Ohm, and VS=6V, thenV2=R1VSR1+R2=635=3.6V.

Resistors in parallel. Current divider circuit and equation


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