Two resistors of resistances R 1 and R 2, with R 2> R 1, are connected to a volt

Question

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 10Is.

Part A

Let r be the ratio R1/R2. Find r.

Round your answer to the nearest thousandth.

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 10Is.

Part A

Let r be the ratio R1/R2. Find r.

Round your answer to the nearest thousandth.

Explanation / Answer

Series: I = Is = V/(R1+R2)

parallel, R = R1*R2/(R1+R2)

Ip = 10*Is = V/R = V(R1+R2)/R1*R2

10V/(R1+R2) = V(R1+R2)/R1*R2

10/(R1+R2) = (R1+R2)/R1*R2

10*R1*R2 = (R1+R2)(R1+R2)

10*R1*R2 = 2R1R2 + R1^2 + R2^2

8R1R2 = R1^2 + R2^2

r = R1/R2

R1 = rR2

8R1R2 = R1^2 + R2^2

8rR2R2 = (rR2)^2 + R2^2

8rR2^2 = (rR2)^2 + R2^2

R2^2 (8r - r^2 - 1) = 0

assuming R2 is not zero

r^2 - 8r + 1 = 0

by solving this

r = 0.127 , 7.87

7.87 is not possible because r = R1/R2 = and R2 > R1 so r will be less than 1

r = 0.127

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