Current Divider
Current split between two parallel resistors.
Formula
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How it works
When a total current enters two resistors in parallel, it divides so that the branch with the smaller resistance carries more current. This happens because both resistors have the same voltage across them, and by Ohm's law the branch current is V/R, so current is inversely proportional to resistance. Starting from I = I_1 + I_2 and V = I_1R_1 = I_2R_2 gives the current-divider relation I_1 = I\frac{R_2}{R_1 + R_2}.
When to use it
Use this when analyzing parallel resistor networks and you know the total current entering the parallel pair. It is especially useful in circuit simplification, sensor networks, biasing networks, and any problem where you need the current in one branch without first solving for the node voltage.
Worked example, step by step
A total current of 12 A enters two parallel resistors: R_1 = 8 \Omega and R_2 = 4 \Omega. Use the current-divider formula for the current through R_1: I_1 = I\frac{R_2}{R_1 + R_2} I_1 = 12\frac{4}{8 + 4} I_1 = 12\frac{4}{12} I_1 = 4 A Find the other branch current as a check: I_2 = I - I_1 = 12 - 4 = 8 A Since the smaller resistor is 4 \Omega, it carries the larger current, which is consistent with the rule.
Common mistakes to avoid
- swapping R_1 and R_2 in the numerator, which gives the current in the wrong branch
- using the formula for series circuits, where current is the same through every element
- forgetting that the denominator is the sum R_1 + R_2, not the product or reciprocal sum
Did You Know?
A current divider splits current between parallel paths in inverse proportion to their resistances.
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