Question

Two resistors have resistances R1 and R2. When the resistors are connected in series to a 12.7-V battery, the current from the battery is 1.81 A. When the resistors are connected in parallel to the battery, the total current from the battery is 9.06 A. Determine R1 and R2. (Enter your answers from smallest to largest.)

Answer 1

Answer:

5.065 Ohm,  1.935 Ohm

Explanation:

when the resistors are connected in series.

Rs = R1 + R2

by using Ohm's law

V  = I Rs

12.7 = 1.81 x Rs

So, R1 + R2 = 7 Ohm      ...... (1)

When the resistors are connected in parallel.

Rp = R1 x R2 / (R1 + R2)

Using Ohm's law

V = I Rp

12.7 = 9.06 x Rp

R1 x R2 / (R1 + R2) = 1.4 ohm

Substitute the value of R1 + R2 from equation (1)

R1 x R2 = 1.4 x 7

R1 x R2 = 9.8

$R1 - R2 = \sqrt{(R1 + R2)^{2}-4R1\times R2}$

$R1 - R2 = \sqrt{(49-39.2)}$

R1 - R2 = 3.13 Ohm    ......(2)

By solving equation (1) and equation (), we get

R1 = 5.065 Ohm

R2 = 1.935 Ohm