# How does the current divide in parallel inductors?

• jangchen
In summary, the conversation discusses the difference between using the current divider rule and using the equation VO = L*dI/dt when solving a problem involving inductors. The current divider rule assumes a steady state solution, which is not applicable in this case as it is a transient problem. The correct answer can be obtained by using the equation VO = L*dI/dt, which is valid for inductors. The difference between the two approaches is that the current divider rule does not properly account for the initial conditions of the problem. The conversation also highlights the importance of understanding the principles behind equations and not blindly applying them without considering the specific conditions of the problem.

#### jangchen

Homework Statement
In the circuit of Fig. 63.82 io(0)=2mA. Determine io(t) and Vo(t) for t>0
Relevant Equations
$$V_O = L*\frac{di}{dt}$$
I apologize using English fluently because I am not an Enlgish speaker.

When I tried to solve this problem, I used current divider rule.

So, $$i_o(t) = \frac{3}{3+5}*4e^{-2t} = 1.5*e^{-2t} A$$

However, This was wrong.

The answer is $$1.5*e^{-2t} + 0.5 A$$

If I use $$V_O = L*\frac{di}{dt}$$ , I can get right answer.

I wonder why there is a difference
between using current divider rule and using $$V_O = L*\frac{di}{dt}$$.

Delta2
The current divider rule assumes a steady state solution. This is a transient problem. The current divider rule doesn't properly account for the initial conditions. At t=0 each inductor has 2A, which isn't consistent with the 3:5 ratio.

jangchen said:
The answer is $$1.5*e^{-2t} + 0.5 A$$

If I use $$V_O = L*\frac{di}{dt}$$ , I can get right answer.

I wonder why there is a difference
between using current divider rule and using $$V_O = L*\frac{di}{dt}$$.
The voltage divider rule is valid for resistors, when the voltage is proportional to the current, U=RI. In case of inductors, this is not true, U=LdI/dt instead.

jangchen and Delta2
DaveE said:
The current divider rule assumes a steady state solution. This is a transient problem. The current divider rule doesn't properly account for the initial conditions. At t=0 each inductor has 2A, which isn't consistent with the 3:5 ratio.
Thank you for your advise! I got what is a steady state right away.

ehild said:
The voltage divider rule is valid for resistors, when the voltage is proportional to the current, U=RI. In case of inductors, this is not true, U=LdI/dt instead.
Oh, I thought current divider was also applied to the inductor. Thank you for your help!

## 1. How do parallel inductors affect the current in a circuit?

The presence of parallel inductors in a circuit causes the current to divide between them, with some portion of the current flowing through each inductor. This is due to the fact that inductors resist changes in current, so when one inductor experiences a change in current, the other inductor will also experience a change in current in the opposite direction to maintain balance.

## 2. Is the current divided equally between parallel inductors?

No, the current is not necessarily divided equally between parallel inductors. The amount of current flowing through each inductor depends on their individual inductance values and the impedance of the circuit.

## 3. How does the current divide in parallel inductors with different inductance values?

The current will divide between parallel inductors with different inductance values in proportion to their respective inductance values. In other words, the inductor with the higher inductance will have more current flowing through it.

## 4. Can the current divide in parallel inductors be controlled?

Yes, the current divide in parallel inductors can be controlled by adjusting the inductance values or the impedance of the circuit. For example, adding a resistor in series with one of the inductors can influence the current division.

## 5. What are the implications of current divide in parallel inductors for circuit design?

The current divide in parallel inductors must be taken into consideration when designing circuits, as it can affect the overall performance and stability of the circuit. It is important to carefully choose the inductance values and placement of parallel inductors to ensure proper current division and minimize any potential issues.