Resistance Comparison P & S

[zmike]

Homework Statement

Two resistors of resistances R1 and R2, with R2 > R1, are connected to a voltage source with voltage V0. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel,the current Ip from the source is equal to 10 Is. Let r be the ratio R1/R2. Find r.

Homework Equations

Ohm's Law : V = IR
R=pL/A
?

The Attempt at a Solution

I sure that I need to use Ohm's Law to compare the resistance but I am not sure how to calculate the resistance of each of them when they were connected in series and then in parallel,

I know that current is conserved but does this mean that both R1 and R2 have the same current while in series and in parallel?

 

[LowlyPion]

Look at the effect of the equivalent resistances.

For series:

Req = R1 + R2

For || :

1/Req = 1/R1 + 1/R2

 

[nlightner]

To solve this problem, we can use the equations V = IR and R = pL/A. In series, the resistors would have a combined resistance of R1 + R2. Since the voltage is the same in both cases, we can set up the equations V = I1(R1 + R2) and V = I2R1, where I1 and I2 are the currents in series and parallel, respectively. From this, we can see that I1 = I2.

In parallel, the resistors have a combined resistance of R1*R2/(R1+R2). Using Ohm's Law, we can set up the equation V = I3(R1*R2/(R1+R2)), where I3 is the current in parallel. Since we are given that Ip = 10Is, we can substitute and solve for r, the ratio of R1/R2. The final equation would be 10Is = I3(R1*R2/(R1+R2)).

Solving for I3, we get I3 = 10Is*(R1+R2)/R1R2. Substituting this into the previous equation, we get V = 10Is*(R1+R2)/R2. We can then solve for r by substituting in the equation R1 = r*R2. This gives us the final equation, V = 10Is*(r+1).

To find the value of r, we can solve for it by rearranging the equation to get r = (V/10Is) - 1. This gives us the value of r in terms of the given values of V, Is, and the ratio of R1/R2.