Solve for Equivalent Resistance - Resistor is shorted?

In summary, the conversation discusses a circuit problem where the solution involves redrawing the circuit and considering a 75 ohm resistor as a short. The individual also shares their attempt at solving the problem without redrawing the circuit and how it resulted in the same answer. The conversation concludes with the confirmation that this method is valid.
  • #1
zr95
25
1

Homework Statement


I'm studying for a test and since this is technically a textbook problem I figured I'd post here to prevent being flagged.
upload_2016-9-25_14-6-36.png

I have the circuit redrawn.
upload_2016-9-25_14-3-32.png


Homework Equations


Series: Req = R1+R2...
Parallel: 1/Req= 1/R1 + 1/R2...

The Attempt at a Solution


I want to understand why when solving this circuit for Req it is (3 || 30) || 7.5 = 2ohms.
According to the solution I'm looking at the 75 ohm resistor is considered a short and no current flows across this? I don't understand why this is the case.

Also I was originally trying to be lazy and solve and just add things up without redrawing the circuit and ended up with 2ohms by doing:
((5||20)+2)||3 = 2ohms
Was this just coincidence?
 
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  • #2
zr95 said:
I want to understand why when solving this circuit for Req it is (3 || 30) || 7.5 = 2ohms.
According to the solution I'm looking at the 75 ohm resistor is considered a short and no current flows across this? I don't understand why this is the case.
That is because the 75 ohm "resistor" is connected in parallel with a zero resistance piece of wire.

zr95 said:
Also I was originally trying to be lazy and solve and just add things up without redrawing the circuit and ended up with 2ohms by doing:
((5||20)+2)||3 = 2ohms
Was this just coincidence?
Nope, its not a coincidence - if you deform the circuit, your consideration is correct.
 
  • Like
Likes zr95
  • #3
You da man. That makes a lot of sense.
 

FAQ: Solve for Equivalent Resistance - Resistor is shorted?

How do you determine the equivalent resistance when a resistor is shorted?

When a resistor is shorted, it essentially becomes a wire with zero resistance. This means that the equivalent resistance of the circuit is equal to the sum of all the other resistances in the circuit. You can calculate this by using the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances.

Can a shorted resistor affect the overall resistance of a circuit?

Yes, a shorted resistor can significantly affect the overall resistance of a circuit. This is because a shorted resistor has a very low resistance, which means that it allows a large amount of current to pass through it. This can cause an increase in the overall current and a decrease in the overall resistance of the circuit.

How does a shorted resistor affect the voltage in a circuit?

A shorted resistor can cause a decrease in the voltage in a circuit. This is because a shorted resistor allows a large amount of current to flow through it, which can cause a voltage drop. This means that the voltage across the rest of the circuit will also decrease.

What are the potential dangers of a shorted resistor?

A shorted resistor can pose several dangers, including overheating and damage to other components in the circuit. When a large amount of current flows through a shorted resistor, it can generate a lot of heat, which can cause the resistor to burn out or even start a fire. Additionally, the excess current can damage other components in the circuit, leading to malfunctions or failures.

How can a shorted resistor be fixed?

The best way to fix a shorted resistor is to replace it with a new one. If the shorted resistor is part of a larger circuit, you may need to disconnect the power source and remove any damaged components before replacing the resistor. It is also important to identify and address the cause of the short circuit to prevent future occurrences.

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