Two unknown resistors. Need to find values of resistors.

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In summary, when two unknown resistors are connected in series with a battery, the battery delivers 260 W and carries a total current of 5.00 A. When connected in parallel, the battery delivers 35.0 W at the same total current. Using the equations P = I^2 x R and Req = R1R2/(R1 + R2), we can solve for the values of the two resistors. The equivalent resistance for the series circuit is 10.4 ohms and for the parallel circuit is 1.4 ohms. Solving the equations R1 + R2 = 10.4 and R1R2/(R1 + R2) = 1.4 gives us the
  • #1
jhart_929
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Homework Statement



When two unknown resistors are connected in series with a battery, the battery delivers 260 W and carries a total current of 5.00 A. For the same total current, 35.0 W is delivered when the resistors are connected in parallel. Determine the values of the two resistors.

Homework Equations



P = I^2 x R

The Attempt at a Solution



I tried to make two unknowns by plugging in numbers into the equations, but that's not working. I know that the voltage will be the same throughout the parallel circuit, and that the current will be the same throughout the series circuit, but I'm not quite sure where to go from there.
 
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  • #2
Since P = I2R, we can solve for the equivalent resistance of the resistors.

Req = P/I2

When the resistors are in series, r1 + r2 = Req

Construct a similar equation for when the resistors are in parallel and you can solve for the values of the two resistors.
 
  • #3
I have my two equations, but I'm having trouble putting the two equations together. I have r1 + r2 = 7 and 1/r1 + 1/r2 = 1/52
 
  • #4
I'm not certain those values are correct, maybe I've made a mistake?

For series I get, Req = P/I2 = (260 W)/(5 A)2 = 10.4 ohms.

For parallel I get, Req = P/I2 = (35 W)/(5 A)2 = 1.4 ohms.

To get you started on solving the two equations, we know that R1 + R2 = 10.4 and R1R2/(R1 + R2) = 1.4. Combine these two equations.
 
  • #5
just solve for r1 and substitute into the other...

but are you sure those figures are correct? how did you get them?
 
  • #6
I think I must have forgotten to square "I"...your figures are correct. But then don't you also have to take into consideration that when you do 1/r1 + 1/r2 , that it equals 1/Req? ?
 
  • #7
Unless I've misunderstood your question which is certainly possible, I believe the equation Req = R1R2/(R1 + R2) takes care of that consideration.
 
  • #8
Oh. Okay. I missed that. Thank you so much!
 
  • #9
No problem!
 

1. How do I find the values of two unknown resistors?

To find the values of two unknown resistors, you will need to use Ohm's Law and a circuit with a known power source, such as a battery. Connect the two resistors in series with each other and measure the voltage across each resistor. Then, use the equation R = V/I to calculate the resistance of each resistor, where R is resistance, V is voltage, and I is current. Once you have the resistance values, you can determine the specific resistance of each resistor by measuring their physical dimensions.

2. What is the relationship between resistance and voltage in a circuit?

The relationship between resistance and voltage is described by Ohm's Law, which states that the voltage across a resistor is directly proportional to the current flowing through it. In other words, as resistance increases, voltage increases, and as resistance decreases, voltage decreases.

3. Can I find the values of two unknown resistors with only one measurement?

No, you will need at least two measurements to find the values of two unknown resistors. This is because Ohm's Law requires both voltage and current to be measured in order to calculate resistance. If you only have one measurement, you can only determine the ratio of the two resistors, but not their individual values.

4. What is the difference between series and parallel circuits?

In a series circuit, all components are connected in a single loop, with the current flowing through each component in succession. In a parallel circuit, components are connected in multiple branches, with the current splitting and flowing through each branch simultaneously. The total resistance of a series circuit is equal to the sum of the individual resistances, while the total resistance of a parallel circuit is less than the smallest individual resistance.

5. How do I measure resistance with a multimeter?

To measure resistance with a multimeter, first turn the dial to the resistance setting (usually denoted by the Greek letter "Ω"). Then, make sure the multimeter leads are not touching each other, and touch them to the ends of the resistor or component you want to measure. The multimeter will display the resistance value in ohms (Ω). It is important to note that the component being measured must be disconnected from any power source for an accurate reading.

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