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D.C. Theory
© copyright
M.J.Morris 2004

6.03 The current divider rule.

The current divider rule can be used as a quick way of calculating branch currents, when a current flows from a junction to two parallel branches.

Proof of the current divider rule.

• I₃ = V_P/R₃ .
• V_P = I_T x R_T .
• R_T = (R₂ x R₃)/(R₂ + R₃) .
• Therefore V_P = I_T x (R₂ x R₃)/(R₂ + R₃) .
• Therefore I₃ = I_T x (R₂ x R₃)/(R₂ + R₃)/R₃ .
• Therefore I₃ = I_T x R₂/(R₂ + R₃) .

Note the format is almost identical to the voltage divider rule, except that the resistor value that is on the top of the resistor ratio in the equation, is not the one we are calculating the current for.