# Calculating Resistance: 3 & 12 Ohm Resistors for 2.4 Ohm Result

• roxas
In summary, the total resistance in parallel is calculated by using the formula 1/Rt = 1/R1 + 1/R2 + 1/R3 + ... and in this case, a combination of 3 and 12 ohm resistors can be used to achieve a specific desired resistance. Any combination of resistors can be used as long as the appropriate formula is followed. Adding more resistors in parallel decreases the total resistance, while using resistors in series results in a total resistance equal to the sum of all individual resistances.
roxas
what is the smallest resistance that can be obtained by using onlu a 3 ohm resistor and a 12 ohm resistor??

i calculATED USING 1/3 = 1/2 AND I GOT 4 OHMS

thx anyway

Okay, if the resistors are placed in series the effective resistance of the system is simply the sum of the individual resistances (i.e. $R_{t}=3+12=15\Omega$).

However, if we place the resitors are placed in parallel the effective resistance of the array is...?

The smallest resistance that can be obtained by using a 3 ohm resistor and a 12 ohm resistor is 2.4 ohms. This is because the total resistance in a series circuit is equal to the sum of all individual resistances. In this case, 3 ohms + 12 ohms = 15 ohms. To obtain a resistance of 2.4 ohms, the two resistors must be connected in parallel. The formula for calculating parallel resistances is 1/Rt = 1/R1 + 1/R2, where Rt is the total resistance and R1 and R2 are the individual resistances. Solving for Rt, we get 1/2.4 = 1/3 + 1/12, which simplifies to 2.4 ohms. It is important to use the correct formula for the circuit configuration in order to obtain the accurate result. In this case, using the formula for parallel resistances is the correct approach. I hope this helps clarify the reason for the 2.4 ohm result.

## 1. How do you calculate the total resistance of 3 and 12 ohm resistors in parallel?

The total resistance in parallel is calculated using the formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 + ... where Rt is the total resistance and R1, R2, R3, etc. are the individual resistances. In this case, we would have 1/Rt = 1/3 + 1/12, which simplifies to 1/Rt = 4/12, or Rt = 3 ohms.

## 2. What is the purpose of using 3 ohm and 12 ohm resistors to get a 2.4 ohm result?

The purpose of using different resistors in parallel is to achieve a specific desired resistance. By using a combination of 3 and 12 ohm resistors, we can create a total resistance of 2.4 ohms, which may be needed for a particular circuit or application.

## 3. Can you use any combination of resistors to get a specific resistance?

Yes, as long as you understand the relationship between resistors in parallel and how to calculate the total resistance. You can use any combination of resistors to achieve a desired resistance, as long as you follow the appropriate formula and take into account the value of each resistor.

## 4. What happens to the total resistance when you add more resistors in parallel?

The total resistance decreases as you add more resistors in parallel. This is because the more paths there are for the current to flow through, the easier it is for the current to pass through the circuit, resulting in a lower overall resistance.

## 5. Can you use resistors in series instead of parallel to achieve a specific resistance?

Yes, resistors can also be connected in series to achieve a specific resistance. In this case, the total resistance is simply the sum of all the individual resistances. However, using resistors in parallel may be more efficient in some cases, as it allows for a lower overall resistance with fewer components.

• Introductory Physics Homework Help
Replies
11
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
29
Views
2K
• Introductory Physics Homework Help
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
778
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
995
• Introductory Physics Homework Help
Replies
3
Views
961