Two resistors have resistances R(smaller) and R(larger), where R(smaller) < R(larger). When the resistors are connected in series to a 12.0-V battery, the current from the battery is 1.78 A. When the resistors are connected in parallel to the battery, the total current from the battery is 11.3 A. Determine the two resistances.

R(smaller) = 1.3 Ω  and  R(larger) = 5.4 Ω

Explanation:

Ohm's Law states that:

V = IR

R = V/I

where,

R = Resistance

V = Potential Difference

I = Current

Therefore, for series connection:

Rs = Vs/Is

where,

Rs = Resistance when connected in series = R(smaller) + R(larger)

Vs = Potential Difference when connected in series = 12 V

Is = Current when connected in series = 1.78 A

Therefore,

R(smaller) + R(larger) = 12 V/1.78 A

R(smaller) + R(larger) = 6.74 Ω   equation 1

R(smaller) = 6.74 Ω - R(larger)     equation 2

Therefore, for series connection:

Rp = Vp/Ip

where,

Rp = Resistance when connected in parallel = [1/R(smaller) + 1/R(larger)]⁻¹

Rp = [{R(smaller) + R(larger)}/{R(smaller).R(larger)]⁻¹

Rp = R(smaller).R(larger)/[R(smaller) + R(larger)]

Vp = Potential Difference when connected in parallel = 12 V

Ip = Current when connected in parallel = 11.3 A

Therefore,

R(smaller).R(larger)/[R(smaller) + R(larger)] = 12 V/11.3 A

using equation 1 and equation 2, we get:

[6.74 Ω - R(larger)].R(larger)/6.74 Ω = 1.06 Ω

6.74 R(larger) - R(larger)² = (6.74)(1.06)

R(larger)² - 6.74 R(larger) + 7.16 = 0

solving this quadratic equation we get:

R(larger) = 5.4 Ω (OR) R(larger) = 1.3 Ω

using these values in equation 2, we get:

R(smaller) = 1.3 Ω (OR) R(smaller) = 5.4 Ω

Since, it is given in the question that R(smaller)<R(larger).

Therefore, the correct answers will be:

R(smaller) = 1.3 Ω  and  R(larger) = 5.4 Ω

hello, i am papaguy.

i have found an answer to your question but use it as information.

information: because weak acids/bases have low concentration of hydrogen ions, the addition of water has a large impact on the ph. 2. a difference in 1 unit is a 10x difference in concentration for example; a liquid with ph of 3 is 10x more acidic than a liquid with a ph of 4. therefore, a liquid with a ph of 3 is stronger.

best of luck!