Arranging resistors to have a minimum equivalent

In summary, the conversation discusses how to find the minimum resistance when connecting 50 resistances of 0.25 ohm each. The relevant equations for connecting resistances in series and parallel are mentioned. It is determined that the minimum resistance is obtained when all resistances are connected in parallel, which should result in an equivalent resistance of 4/50 ohms. However, the given answer is 1/200 ohms, indicating a math error. The conversation concludes with the suggestion to slow down and check calculations, resulting in the correct answer.
  • #1
Tanishq Nandan
122
5

Homework Statement



The minimum resistance obtained by connecting 50 resistances of 0.25 ohm each is
A)50/4ohm B)4/50 ohm C)200 ohm D)1/200 ohm
2.Relevant equations
1.When resistances are connected in series,
▪R(equivalent)=summation of all individual resistances
2.When resistances are connected in parallel ,
▪1/(equivalent resistance) =1/(summation of reciprocals of individual resistances)

The Attempt at a Solution


Minimum resistance is usually obtained when all resistances are connected in parallel (better than adding them all up).
So,it should be coming as 4/50 ohms,using formula 2,but the answer is given as D,1/200 ohms.

How do you arrange these resistors to have an equivalent resistance of 1/200 ohms??
 
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  • #2
You have made a simple math error. Slow down and do it again. Show more intermediate steps if you want to know exactly which step is in error.
Tanishq Nandan said:
How do you arrange these resistors to have an equivalent resistance of 1/200 ohms??
You were correct when you said they should all be in parallel.
 
  • #3
I got D as well. Check your calculations.
 
  • #4
Yeah,got it,dumb me.Thanks,guys..
 

What is the purpose of arranging resistors to have a minimum equivalent?

The purpose of arranging resistors to have a minimum equivalent is to achieve a desired resistance value in a circuit while using the least number of resistors possible. This can help simplify the circuit design and reduce cost.

How do you calculate the minimum equivalent resistance of a circuit?

To calculate the minimum equivalent resistance of a circuit, you need to determine the values of all the resistors in the circuit and then use the appropriate formula based on their arrangement (series or parallel). For resistors in series, the equivalent resistance is the sum of all the individual resistances. For resistors in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each individual resistance.

What is the difference between series and parallel arrangements of resistors?

In a series arrangement, the resistors are connected one after the other, so the current passing through each resistor is the same. In a parallel arrangement, the resistors are connected side by side, so the voltage across each resistor is the same. Additionally, in a series arrangement, the total resistance is the sum of all the individual resistances, while in a parallel arrangement, the total resistance is less than the smallest individual resistance.

Can you have a circuit with both series and parallel arrangements of resistors?

Yes, it is possible to have a circuit with both series and parallel arrangements of resistors. This is known as a combination circuit. In this type of circuit, you can simplify the circuit by first finding the equivalent resistance of the series resistors and then finding the equivalent resistance of the parallel resistors. Finally, you can use these equivalent resistances to calculate the total resistance of the circuit.

What factors should be considered when arranging resistors to have a minimum equivalent?

When arranging resistors to have a minimum equivalent, you should consider the desired resistance value, the available resistors with their respective values, and the type of circuit (series, parallel, or combination). It is also important to consider the power ratings and tolerances of the resistors to ensure they can handle the current and provide accurate results in the circuit.

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