Find Ratio of Resistors R_1/R_2

[Milquetoast]

Homework Statement

Two resistors of resistances R_1 and R_2, with R_2 > R_1, are connected to a voltage source with voltage V_0. When the resistors are connected in series, the current is I_s. When the resistors are connected in parallel, the current I_p from the source is equal to 10 I_s.

Let r be the ratio R_1 / R_2. Find r.

Homework Equations

In series R = R1 + ... + RN
In parallel 1 / R = 1 / R1 + ... + 1 / RN

The Attempt at a Solution

I_s (R_1 + R_2) = 10 I_s (R_1 * R_2) / (R_1 + R_2)

0 = R_1^2 - 8 R_1 R_2 + R_2^2

Quadraxtic equation R_1 = 4 +/- sqrt(9 - R_2)

I don't know quite what to do now

I need that ratio but it is just dirty

(4 + sqrt(9 - R_2)) / R_2

Help very much appreciated

 

[Shooting Star]

0 = R_1^2 - 8 R_1 R_2 + R_2^2

Dividing by R2^2,

r^2 - 8r + 1 = 0.

Solve for r.

 

[Moetasim]

I would approach this problem by first rearranging the given equations to solve for the ratio R_1/R_2. In series, we know that R = R_1 + R_2, so R_1/R_2 = (R - R_2)/R_2. Similarly, in parallel, we have 1/R = 1/R_1 + 1/R_2, so R_1/R_2 = (1/R - 1/R_2)/1/R_2.

Next, I would substitute the given values into these equations. In series, R = V_0/I_s, so R_1/R_2 = (V_0/I_s - R_2)/R_2. In parallel, 1/R = V_0/I_p, so R_1/R_2 = (1/(V_0/I_p) - 1/R_2)/1/R_2.

Finally, I would set these two expressions equal to each other and solve for R_1/R_2. This would give us the desired ratio r.