Two resistors have resistances R1 and R2. When the resistors are connected in series to a 12.4-V battery, the current from the battery is 2.13 A. When the resistors are connected in parallel to the battery, the total current from the battery is 9.01 A. Determine R1 and R2. (Enter your answers from smallest to largest.)

Question

Two resistors have resistances R1 and R2. When the resistors are connected in series to a 12.4-V battery, the current from the battery is 2.13 A. When the resistors are connected in parallel to the battery, the total current from the battery is 9.01 A. Determine R1 and R2. (Enter your answers from smallest to largest.)

I have tried this, by finding the combined R and don't know where to go from there.

Thank you!

Answer 1

R1+R2=12.4/2.13

1/R1 +1/R2=conductnce=9.01/12.4

now solve for R1 in the first equation in terms of R2, then put that into the second equation, solve for R2.

A little bit of algebra fractions is involved.

Answer 2

Eq1: R1+R2 = E/I = 12.4/2.13 = 5.82 Ohms

(R1*R2)/(R1+R2) = 12.4/9.01 = 1.38 Ohms
Replace R1+R2 with 5.82 Ohms:
R1*R2/5.82 = 1.38
R1*R2 = 5.82*1.38 = 8.0
R1 = 8/R2

In Eq1, replace R1 with 8/R2:
8/R2 + R2 = 5.82
8 + R2^2 = 5.82R2
R2^2 - 5.82R2 + 8 = 0
Use Quadratic Formula.
R2 = 3.59 Ohms

In Eq1, replace R2 with 3.59 Ohms
R1 + 3.59 = 5.82
R1 = 2.23 Ohms

Answer 3

To solve this problem, we will use the formulas for resistors in series and parallel circuits.

1. Resistors in series: The total resistance (Rs) of resistors in series is equal to the sum of their individual resistances.
Rs = R1 + R2

2. Resistors in parallel: The reciprocal of the total resistance (Rp) of resistors in parallel is equal to the sum of the reciprocals of their individual resistances.
1/Rp = (1/R1) + (1/R2)

Given:
Voltage (V) = 12.4 V
Current in series (Is) = 2.13 A
Current in parallel (Ip) = 9.01 A

Step 1: Solve for R1 and R2 in the series circuit.
Using Ohm's Law (V = I * Rs), we can calculate the total resistance in the series circuit.
12.4 V = 2.13 A * Rs
Rs = 12.4 V / 2.13 A
Rs = 5.81 Ω

Since resistors in series add up their resistances, we have:
Rs = R1 + R2
5.81 Ω = R1 + R2

Step 2: Solve for R1 and R2 in the parallel circuit.
Using Ohm's Law (V = I * Rp), we can calculate the total resistance in the parallel circuit.
12.4 V = 9.01 A * Rp
Rp = 12.4 V / 9.01 A
Rp = 1.376 Ω

Using the formula for resistors in parallel:
1/Rp = (1/R1) + (1/R2)
1/1.376 Ω = (1/R1) + (1/R2)

Now we have a system of equations:
5.81 Ω = R1 + R2
1/1.376 Ω = (1/R1) + (1/R2)

Step 3: Solving the system of equations.
Rearrange the second equation to solve for R2:
1/1.376 Ω - (1/R1) = 1/R2
1/R2 = 1/1.376 Ω - (1/R1)

Substitute R2 with (5.81 Ω - R1) in the rearranged equation:
1/R2 = 1/1.376 Ω - (1/R1)
1/(5.81 Ω - R1) = 1/1.376 Ω - (1/R1)

Multiply both sides by (5.81 Ω - R1)(1/1.376 Ω):
1 = (5.81 Ω - R1)(1/1.376 Ω) - (5.81 Ω - R1)(1/R1)

Simplify the equation:
1 = (5.81/1.376 - R1/1.376) Ω - (5.81 Ω/R1 - R1/R1)
1 = 4.22 - 3.37R1

Rearrange the equation to solve for R1:
3.37R1 = 4.22 - 1
3.37R1 = 3.22
R1 = 3.22 Ω

Now substitute the value of R1 back into the equation to solve for R2:
5.81 Ω = R1 + R2
5.81 Ω = 3.22 Ω + R2
R2 = 5.81 Ω - 3.22 Ω
R2 = 2.59 Ω

Therefore, the values of R1 and R2 are 3.22 Ω and 2.59 Ω, respectively.

Answer 4

To solve this problem, we can use the equations that relate resistance, current, and voltage in series and parallel circuits.

First, let's find the combined resistance of the resistors when they are connected in series. In a series circuit, the total resistance is the sum of the individual resistances:

R_total = R1 + R2

Given that the current from the battery in the series circuit is 2.13 A, and the voltage across the resistors is 12.4 V, we can use Ohm's Law to find the total resistance:

R_total = V / I
R_total = 12.4 V / 2.13 A
R_total ≈ 5.81 Ω

Now, let's find the combined resistance of the resistors when they are connected in parallel. In a parallel circuit, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances:

1 / R_total = 1 / R1 + 1 / R2

Given that the total current from the battery in the parallel circuit is 9.01 A, we can use Ohm's Law to find the total resistance:

R_total = V / I
R_total = 12.4 V / 9.01 A
R_total ≈ 1.375 Ω

Now, we can set up a system of equations to solve for R1 and R2:

{
R1 + R2 = 5.81
1 / R1 + 1 / R2 = 1 / R_total
}

Solving this system of equations will give us the values of R1 and R2. One way to solve this system is by substitution. Rearrange the first equation to solve for R2:

R2 = 5.81 - R1

Substitute this expression for R2 in the second equation:

1 / R1 + 1 / (5.81 - R1) = 1 / R_total

Now, you can solve this equation to find the values of R1 and R2.