Complete Electronics Self-Teaching Guide with Projects

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.

Figure 1.9

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

Questions

Which of the following relationships are valid for this circuit?

A. V_S = R₁I₁

B. V_S = 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:

3. From the fact that I_T = I₁ + I₂, express I_T 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?

Figure 1.10

Answers

Work through the steps as shown here:

1. I₁/I₂ = R₂/R₁ = 1/2

2. I₂ = 2I₁

3. I_T = I₁ + I₂ = I₁ + 2I₁ = 3I₁

4. I₁ = I_T/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 ...