Find the Equivalent Resistance of a Network

In summary, a network consists of a combination of parallel and series connections. The equivalent resistance of the network is 1/5 + 1/3 = 0.533, and 1/0.533 = 1.875.
  • #1
jumbogala
423
4

Homework Statement


A network consists of a combination of parallel and series connections. What is the equivalent resistance of the network? (Hint: Use the series and parallel resistance formulas).

The network looks like this:
resistance.jpg

Homework Equations


When a circuit is in series, R = R1 + R2 + R3...

When a circuit is in parallel, R = 1/R1 + 1/R2 + 1/R3...

The Attempt at a Solution


First, c and b are in series, so I just add them up. 5 + 3 = 8.

Now, a, d, and this new resistor of value 8 are in series. So add them up again.
8 + 4 + 1 = 13.

Did I do that correctly?
 
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  • #2
Sorry. B and C are ||.

Not in series.
 
  • #3
They look like they're in series to me... how can you tell?

That changes my answer to 1/5 + 1/3 = 0.533. And 1/0.533 = 1.875.

Then 1.875 + 4 + 1 = 6.875
 
  • #4
jumbogala said:
They look like they're in series to me... how can you tell?

That changes my answer to 1/5 + 1/3 = 0.533. And 1/0.533 = 1.875.

Then 1.875 + 4 + 1 = 6.875

That looks more like it.
 
  • #5
jumbogala said:
When a circuit is in parallel, R = 1/R1 + 1/R2 + 1/R3...

This is wrong. I think you meant to write:
1/Req = 1/R1 + 1/R2 + 1/R3...

They look like they're in series to me... how can you tell?
Notice that the upper terminals of C and B share a common node. Similarly, the bottom terminals of C and B share a common node.
 
  • #6
Yeah, I meant to write 1/Req = 1/R1 + 1/R2...

So a is in series with c because it only shares one common node? And b and c are in parallel because they share two nodes?
 
  • #7
So a is in series with c because it only shares one common node? And b and c are in parallel because they share two nodes?
Well, a better way to say it is this: A is in series with the combination C||B.

If the same current flows through two resistive elements, the elements are in series.
If the same voltage potential is across two elements, the elements are in parallel.

Does that help?
 
  • #8
That helps a lot - I understand now. Thank you!
 

FAQ: Find the Equivalent Resistance of a Network

How do I determine the equivalent resistance of a network?

To determine the equivalent resistance of a network, you need to first draw a circuit diagram and identify the individual resistors. Then, use the appropriate formula (series or parallel) to calculate the total resistance of the network.

What is the difference between series and parallel circuits?

A series circuit has all components connected in a single loop, while a parallel circuit has multiple branches with components connected in parallel. In a series circuit, the current remains constant throughout, while in a parallel circuit, the voltage remains constant.

Can resistors be combined in both series and parallel?

Yes, it is possible to combine resistors in both series and parallel to create a more complex network. This is known as a combination circuit.

How does the number of resistors affect the equivalent resistance of a network?

In a series circuit, the equivalent resistance increases with each additional resistor, while in a parallel circuit, the equivalent resistance decreases with each additional resistor. The total number of resistors in a network can greatly affect the overall resistance.

Can I use the same formula to calculate the equivalent resistance for any network?

No, the formula used to calculate the equivalent resistance of a network depends on the specific circuit configuration. For example, the formula for a series circuit is different from that of a parallel circuit. It is important to correctly identify the circuit type before using the appropriate formula.

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