# Can't find total resistance in a complex star circuit

• Chrys
In summary, the student is trying to find the time constant for a RL circuit. They know that a time constant in a RL circuit is t=L/R, but they can't find the Rtotal because it is in a star direction. They use Thevenin's theorem to find the equivalent series resistance and find that the time constant is 0.1s.

#### Chrys

[Thread moved from the technical forums to the schoolwork forums by the Mentors]

Hi i have this assignment for homework:

There is only one battery for the circuit, E=10V, R=4 Ohms and L=1H
it asks me to find the time constant of the circuit. i know that a time constant in a RL circuit is t=L/R
but i can't find the Rtotal since its in a star direction.

Thanks!

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Delta2
So you have to analyze the circuit completely. So you should start to write down the differential equations for the relevant voltages and currents!

what do you mean? i am kind of bad at physics
and in my university we just started learning integrals

Delta2
There are basically two ways to solve this problem.

1. formal and rigorous approach
Write the system of differential equations for this circuit using Kirchhoff's laws, then simplify the differential equations to find the time constant

2. Fast methods commonly used in engineering
Use Thevenin's theorem to quickly find the equivalent series resistance, and then directly write the time constant.

Delta2, hutchphd, DaveE and 1 other person
Chrys said:
Hi i have this assignment for homework:
Hi @Chrys. Welcome to PF. Your question might be better in the 'Introductory Physics Homework Help' section. Maybe one of the mentors will move it there.

The rules here require that you show evidence of your own effort before we offer guidance. See https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

However, to help you get started, I will just say two words: Thevenin’s Theorem!

Edit. Aha! @alan123hk beat me to it by a few nanoseconds!

berkeman
Steve4Physics said:
beat me to it by a few nanoseconds!
I'm sorry for that, I didn't mean to

Delta2 and Steve4Physics
alan123hk said:
I'm sorry for that, I didn't mean to

and in my circuit what is my load resistor?

Chrys said:
and in my circuit what is my load resistor?
Treat the inductor as the (Thevenin) load. Show us your working and we will look it over.

(Thevenin's theorem isn't just limited to resistors. Do a bit of background reading/research for yourself - you are at university level now!)

Chrys said:
I've reached till here but i don't know how to continue...
You have correctly calculated the Thevenin voltage as ##V_{Th} = 5V##. (If you used the voltage (potential) divider formula, you could have done it without first finding the current.)

However, you don’t actually need ##V_{Th}## to answer this question!

And note that in your final diagram, you should show the (Thevenin) supply voltage as 5V, not 10V.

You have correctly found the Thevenin resistance to be ##R_{Th} = 10Ω##.

***To find the time constant, you now pretend the circuit is simply a battery, 10Ω resistor and 1H inductor in series.***

What is the standard formula for the time constant of an RL series circuit?

hutchphd
time constant in a RL circuit is t=R/L, in my final circuit the battery should be 5V right?

Chrys said:
time constant in a RL circuit is t=R/L, in my final circuit the battery should be 5V right?
Yes. Your Thevenin equivalent circuit is a 5V supply, a 10Ω resistor and a 1H inductor all in series. But the voltage is not needed if all you want to do is to find the time constant.

So the time constant is ?

0,1s. Later on in the excersice it asks me to find something else with time=10 time constant, it should be 1s right?

Steve4Physics
Chrys said:
0,1s. Later on in the excersice it asks me to find something else with time=10 time constant, it should be 1s right?
Yes and yes.

It's good practice to show all working clearly:
##\tau = \frac L {R_{Th}} = \frac {1H} {10\Omega} = 0.1s##
(Here in the UK we use a dot to represent the decimal position.)

Chrys said:
0,1s. Later on in the excersice it asks me to find something else with time=10 time constant, it should be 1s right?
In my opinion the constant has to be -0.1 s.

In my opinion the constant has to be -0.1 s.
Do you mean the time constant should be negative?
Can you explain further?

I remember in my previous study and work experience that when we referred to the time constant by itself, we simply represented it as a positive number (L/R)).

 If Ic=0.5*(1-e^(-10*t)) then the time constant it is 1/-10=-0.1​

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i think that using basic power properties its 1/(e^(10*t)) and we write e^(-10*t) because its more simple to the eye. Also how would you explain and use negative time?!?

 If Ic=0.5*(1-e^(-10*t)) then the time constant it is 1/-10=-0.1​
If ##\tau## is the time constant, the exponential decay factor is written as:
##e^{- \frac t {\tau}}##

This is the ‘standard format’, the minus sign is always present.
Both time (##t##) and the time constant (##\tau##) are positive quantities.

For example if we write:
##e^{- \frac t {0.1}}##
we are using ##\tau= 0.1## not ##\tau= -0.1##.

Steve4Physics said:
the exponential decay factor
Yes. And in the real world, decay is the usual direction. Sometimes one talks about an exponential growth factor. The issue is Semantic and contextual. The "time constant" is a positive number by tacit agreement.

## 1. How do I calculate the total resistance in a complex star circuit?

The total resistance in a complex star circuit can be calculated by adding the reciprocals of the individual resistances and then taking the reciprocal of the sum. This is known as the parallel resistance formula.

## 2. Why is it difficult to find the total resistance in a complex star circuit?

Finding the total resistance in a complex star circuit can be difficult because it involves multiple resistors connected in a combination of series and parallel. This makes it challenging to determine the equivalent resistance of the circuit.

## 3. Can I use Ohm's law to find the total resistance in a complex star circuit?

No, Ohm's law cannot be directly applied to find the total resistance in a complex star circuit. Ohm's law only applies to simple circuits with one resistor and a single path for current flow.

## 4. Are there any shortcuts or tricks to finding the total resistance in a complex star circuit?

Yes, there are some shortcuts or tricks that can be used to find the total resistance in a complex star circuit. One method is to first simplify the circuit by combining resistors in series or parallel, and then using the parallel resistance formula to find the total resistance.

## 5. Can I use a multimeter to measure the total resistance in a complex star circuit?

Yes, a multimeter can be used to measure the total resistance in a complex star circuit. However, the circuit must be disconnected from any power source and all components must be removed before making the measurement.