How to Determine the Current Flow in a Parallel Circuit
A basic question in introductory physics courses asks students to determine the current through each branch of a parallel circuit. One configuration of such a circuit places resistors R1 and R2 on separate but parallel wires that combine into a single wire at both ends to contact the ends of a battery of known voltage V. As discussed in Halliday and Resnick's "Fundamentals of Physics," various rules restrict the possible current values I1 and I2 through the resistors, such as the definition of resistance (R=V/I) and Kirchhoff's loop rule.
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Instructions
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Determine the effective resistance of the two parallel resistors R1 and R2 according to the configuration described in the introduction. The formula is:
1/Reff = 1/R1 + 1/R2
For example, if R1=1 ohm and R2=2 ohms, then Reff=2/3.
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2
Determine the current through the circuit between the parallel section where the circuit splits off and the battery source. In other words, find the current where the wire is not running in parallel. Since Reff is the only resistance, use the definition of resistance, V=IR. This gives I=V/Reff, which is easy to solve since V is known beforehand. Note that the current before and after the parallel section, the current has to be the same because the electron count is conserved.
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3
Use Kirchhoff's loop rule to determine the current through R1 and R2. The loop rule says the voltage drop must be the same for any closed loop from the negative to the positive terminal of the battery. Therefore, the voltage drop through R1 and R2 is equal. Since R1 and R2 are the only source of resistance in this example, V is the voltage drop through both R1 and R2. Therefore, the currents are determined by the definition of resistance: I1=V/R1 and I2=V/R2.
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