2 Resistors in Parallel versus in Series

In summary, to find the resistance of the second resistor in a series-parallel circuit with two resistors, one of which is 2.0 kΩ and the other unknown, you can use the formula P = I^2 R to find the power for the resistors in series, and then P = V^2/R to find the power for the resistors in parallel. Setting these two equations equal to each other and solving for the unknown resistance yields a value of 1.56 kΩ. This approach may require solving a quadratic equation.
  • #1
mlostrac
83
0

Homework Statement


Two resistors when connected in series to a 110 V line use one-fourth the power
that is used when they are connected in parallel. If one resistor is 2.0 kΩ, what is the resistance of the other?


Homework Equations



V=IR

The Attempt at a Solution


v=ir

110=i(2000+x)

110=1/4(2000+x)

440=2000+x

x=440-2000

x=-1560

snce x= 1560

the value of another resistance is 1.56 kilo ohm

Did I do that right?
 
Physics news on Phys.org
  • #2
Not quite. Okay, your series formula is fine. But now you have to get the power for the resistors in series. P=I^2 R and P=V^2/R.

Now that you have the power for the series resistors, find the power for the resistors if they were in parallel. 110=i*Req again, but different Req this time.
 
  • #3
Can I just cancel the V's out and solve like this:

R2 + 2000 = 2*(2000*R2)/(2000 + R2)

Which looks like it would require the quadratic eqn
 

Related to 2 Resistors in Parallel versus in Series

1. What is the difference between resistors in parallel and resistors in series?

When resistors are connected in series, they are connected end-to-end, meaning that the current flowing through one resistor must also flow through the other resistors. In contrast, resistors in parallel are connected side-by-side, meaning that the same voltage is applied across each resistor and the total current is divided among them.

2. How does the total resistance change when resistors are in parallel versus in series?

When resistors are connected in series, the total resistance is equal to the sum of each individual resistance. In contrast, when resistors are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of each individual resistance.

3. Which configuration, parallel or series, is better for reducing overall resistance?

Resistors in parallel have a lower total resistance than resistors in series. This means that parallel configurations are better for reducing overall resistance.

4. How does the current flow change in resistors connected in parallel versus in series?

In a series configuration, the current is the same through each resistor. In a parallel configuration, the current is divided among the resistors, with each resistor receiving a portion of the total current.

5. Can I mix resistors in parallel and series in the same circuit?

Yes, it is possible to have a combination of resistors in parallel and series in the same circuit. However, the overall resistance and current flow will be affected by the arrangement of the resistors. It is important to calculate the total resistance and current in the circuit to ensure proper functioning.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
598
  • Introductory Physics Homework Help
Replies
20
Views
470
  • Introductory Physics Homework Help
Replies
3
Views
949
  • Introductory Physics Homework Help
Replies
24
Views
4K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top