In this lesson, you will create a smaller current from a bigger current with parallel resistors.
Resistors in parallel
Voltage and parallel resistors
When two resistors, R1 and R2, are connected in parallel, the voltages across the resistors are identical.
\[V = V_{1} = V_{2}\]Current and parallel resistors
Each current thorough a resistor is:
\[I_{1} = { V_{1} \over R_{1} } = { V \over R_{1} }\] \[I_{2} = { V_{2} \over R_{2} } = { V \over R_{2} }\]For example, when $ V = 10 V $, $ R_{1} = 10 ohm $, and $ R_{2} = 20 ohm $,
\[I_{1} = { V \over R_{1} } = { 10 V \over 10 ohm } = 1 (A)\] \[I_{2} = { V \over R_{2} } = { 10 V \over 20 ohm } = 0.5 (A)\]When $ R_{1} = R_{2} $, the same amount of current flows.
\[I_{1} = { V_{1} \over R_{1} } = { V \over R_{1} }\] \[I_{2} = { V_{2} \over R_{2} } = { V \over R_{1} }\] \[I_{1} = I_{2}\]The total current is:
\[I_{total} = I_{1} + I_{2} = { V \over R_{1} } + { V \over R_{2} }\] \[I_{total} = I_{1} + I_{2} = 1 A + 0.5 A = 1.5 (A)\]Resistance and parallel resistors
The total resistance is:
\[R_{total} = { V \over I } = { V \over I_{total} } = { V \over { { V \over R_{1} } + { V \over R_{2} } } }\] \[{ R_{total} } = { 1 \over { 1 \over R_{1} } + { 1 \over R_{2} } }\] \[{ R_{total} } = { V \over I_{total} } = { 1 \over { 1 \over 10 ohm } + { 1 \over 20 ohm } } = { 10 \over 1.5 } \approx 6.666 (ohm)\]Quick formulas
With $ N $ resistors:
\[{ R_{total} } = { 1 \over { 1 \over R_{1} } + { 1 \over R_{2} } + \dots + { 1 \over R_{N} } }\]With two resistors:
\[R_{total} = { 1 \over { 1 \over R_{1} } + { 1 \over R_{2} } } = { { R_{1} \times R_{2} } \over { R_{1} + R_{2} } }\]Other lessons
Other lessons in Electronics Basic Course: