# Finding the equivalent resistance of an RL cct & step input

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1. Mar 11, 2015

### sugz

1. The problem statement, all variables and given/known data

Determine the inductor current i(t) for both t<0 and t>0 for the circuit shown in the attached document"Circuit 1.

2. Relevant equations

3. The attempt at a solution

Before t=0, i=(25)/(3+2) = 5A
After t=0, i(t)=i(0)e^(-t/tow)
tow=L/R=4/(6/5)

However, the solution states that the equivalent resistance of the circuit is 2, whereas I got 6/5. I am not sure how they were able to get this. Can someone help?

#### Attached Files:

• ###### Circuit 1.PNG
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2. Mar 11, 2015

### axmls

After t = 0, the switch closes, so the left half of the circuit is short circuited. Since you need the equivalent resistance seen from the terminals of the inductor, and since the 3 Ohm resistor is part of the short-circuited loop, there's only the 2 Ohm resistor to account for.

3. Mar 11, 2015

### axmls

Or let me put it this way. Write a Thevenin equivalent of the left loop, with the terminals slightly to the right of the short circuit. That should make it easier to see.

4. Mar 11, 2015

### sugz

Why is it that when you short circuit the voltage source, you ignore the 3 ohm resistor as well? The circuit I get is attached in the file

#### Attached Files:

• ###### 20150311_222746.jpg
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5. Mar 11, 2015

### axmls

Check your Thevenin resistance again. If you attached a voltage source to the terminals, what would happen? Would there be a voltage difference across the resistor? Would the resistor affect anything?

6. Mar 11, 2015

### sugz

Wouldn't there be a voltage difference across the 3 ohm resistor?

7. Mar 11, 2015

### axmls

From Ohm's law, V = IR. So you want the voltage across the resistor. Well, you know the resistance. So what's the current through the resistor?

Or perhaps no current would ever travel through the resistor if there's another path to take that has 0 resistance...hint hint

So in other words, does the resistor have a potential difference across it?

8. Mar 12, 2015

### Staff: Mentor

Sketch the circuit given, and draw a closed loop showing the path that current through the inductor follows after the switch has been closed.