Current Divider PDF
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Summary
This document describes the concepts of current dividers in electrical circuits. It explains how current is divided in series and parallel circuits using formulas, and includes sample calculations showing how the current can be divided through resistors.
Full Transcript
# Current Divider - **Series** - Current is the same. - Different voltage. - **Parallel** - Current is different. - Voltage is the same. **Resistors in Parallel:** $R_{eq} = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}} = \frac{R_1R_2R_3}{R_2R_3+R_1R_3+R_1R_2}$ **By Ohm...
# Current Divider - **Series** - Current is the same. - Different voltage. - **Parallel** - Current is different. - Voltage is the same. **Resistors in Parallel:** $R_{eq} = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}} = \frac{R_1R_2R_3}{R_2R_3+R_1R_3+R_1R_2}$ **By Ohm's Law V=IR** $V = I * R_{eq}$ $I = \frac{V}{R_{eq}} = \frac{V}{\frac{R_1R_2R_3}{R_2R_3+R_1R_3R_1R_2}}$ $I = V * \frac{R_2R_3+R_1R_3+R_1R_2}{R_1R_2R_3}$ $I = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3}$ $I = \frac{I_1R_1 + I_2R_2 + I_3R_3}{R_1}$ $I_1 = \frac{R_2R_3}{R_2R_3 + R_1R_3+R_1R_2} * I\ $I_2 = \frac{R_1R_3}{R_2R_3 + R_1R_3+R_1R_2} * I$ $$I_1 = \frac{R_2R_3}{R_2R_3 + R_1R_3+R_1R_2} * I\ $$ **For I =** $\frac{V}{R}$ **For I2 =** $\frac{V}{R_2}$ $I = \frac{1}{R_1} * I_1R_1$ $I_2 = \frac{1}{R_2} * I_2R_2$ $I = \frac{R_2R_3}{R_2R_3+R_1R_3+R_1R_2} * I$ $I_2 = \frac{R_1R_3}{R_2R_3+R_1R_3+R_1R_2} * I$ $I_1 = \frac{10 * 12}{10+12+10} * 10$ $I_2 = \frac{2 * 10}{2+10+10} * 10$ $I_1 = 10 A$ $I_2 = 2 A$
