The Current Divider

27 In the circuit shown in Figure 1.9, the current splits or divides between the two resistors that are connected in parallel.

IT splits into the individual currents I1 and I2, and then these recombine to form IT.

Questions

Which of the following relationships are valid for this circuit?

A. VS = R1I1
B. VS = R2I2
C. R1I1 = R2I2
D. I1/I2 = R2/R1
Answers

All of them are valid.

28 When solving current divider problems, follow these steps:

1. Set up the ratio of the resistors and currents:

I1/I2 = R2/R1

2. Rearrange the ratio to give I2 in terms of I1:

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3. From the fact that IT = I1 + I2, express IT in terms of I1 only.
4. Now, find I1.
5. Now, find the remaining current (I2).
Question

The values of two resistors in parallel and the total current flowing through the circuit are shown in Figure 1.10. What is the current through each individual resistor?

Answers

Work through the steps as shown here:

1. I1/I2 = R2/R1 = 1/2
2. I2 = 2I1
3. IT = I1 + I2 = I1 + 2I1 = 3I1
4. I1 = IT/3 = 2/3 ampere
5. I2 = 2I1 = 4/3 amperes

29 Now, try these problems. In each case, the total current and the two resistors ...

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