Magnitude of the greater of 2 resistors?

[Bearbull24.5]

Homework Statement

A 20 V emf is placed across 2 resistors in a series, a current of 2 A is present in each of the resistors. When the same emf is placed across the same 2 resistors in parallel, the current through the emf is 10 A. What is the magnitude of the greater of the 2 resistances?

Homework Equations

Series- I=I1=I2
delta V=I1R1+I2R2
Parallel- I=I1+I2

The Attempt at a Solution

I attempted to use the delta V equation, slightly off in my answer

 

[Delphi51]

There is no way to tell if you made a little mistake - you haven't shown your work.

 

[Bearbull24.5]

This was a question from a previous test and the work I have down is scrambled and makes little sense. Those were the equations I could pick out and I'm not even sure if I came up with my answer by working it through or I just picked an answer.

 

[berkeman]

Homework Statement

A 20 V emf is placed across 2 resistors in a series, a current of 2 A is present in each of the resistors. When the same emf is placed across the same 2 resistors in parallel, the current through the emf is 10 A. What is the magnitude of the greater of the 2 resistances?

Homework Equations

Series- I=I1=I2
delta V=I1R1+I2R2
Parallel- I=I1+I2

The Attempt at a Solution

I attempted to use the delta V equation, slightly off in my answer

I don't know what a delta-V equation is.

Just write the two equations for the two cases given. You end up with two equations and two unknowns (R1 and R2). Solve for R2, and you get a quadratic equation. Solve the quadratic equation, and plug that back into the first equation to get R1.

Could you please show us work along the lines of what I've outlined for you?

 

[rwisz]

.

I would first clarify the units for the given values. The emf of 20 V is a measure of potential difference, while the current of 2 A and 10 A is a measure of electric current. This is important to note as the units for resistance are measured in volts per ampere (V/A), also known as ohms (Ω).

Using the given information, we can set up two equations for the series and parallel circuits:

Series: 20 V = 2 A (R1 + R2)
Parallel: 20 V = 10 A (R1 || R2)

Solving for the resistance in each equation, we get:
R1 + R2 = 10 Ω
(R1 || R2) = 2 Ω

To find the magnitude of the greater resistance, we can compare the two equations and see that the resistance in the parallel circuit is smaller than the total resistance in the series circuit. Therefore, the greater resistance must be in the series circuit.

Thus, the magnitude of the greater resistance is 10 Ω.