Math Problem Statement

The electrical current in a circuit with two resistors in series can be expressed as I= V R1+R2 , where V is the total voltage, R1 is the resistance of the first resistor, and R2 is the resistance of the second resistor. Which shows the equation solved for the resistance of the second resistor, R2?

Solution

The given equation for electrical current II in a circuit with two resistors in series is:

I=VR1+R2I = \frac{V}{R_1 + R_2}

To solve for R2R_2, follow these steps:

Step 1: Multiply both sides by R1+R2R_1 + R_2

I(R1+R2)=VI(R_1 + R_2) = V

Step 2: Divide both sides by II to isolate R1+R2R_1 + R_2

R1+R2=VIR_1 + R_2 = \frac{V}{I}

Step 3: Subtract R1R_1 from both sides to solve for R2R_2

R2=VIR1R_2 = \frac{V}{I} - R_1

Thus, the equation solved for R2R_2 is:

R2=VIR1R_2 = \frac{V}{I} - R_1

Would you like a more detailed breakdown of these steps or any specific questions answered?

Here are 5 related questions to explore further:

  1. How does changing R1R_1 or R2R_2 affect the total current in the circuit?
  2. How can you calculate the total resistance in a parallel circuit?
  3. What is the relationship between voltage, current, and resistance in Ohm's law?
  4. How do you calculate the power dissipated by a resistor in a circuit?
  5. What happens to the total resistance when resistors are connected in parallel vs. series?

Tip: Always ensure units are consistent when using formulas involving voltage, current, and resistance. For example, use ohms (Ω\Omega) for resistance, volts (V) for voltage, and amperes (A) for current.

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Math Problem Analysis

Mathematical Concepts

Algebra
Electrical Circuits
Ohm's Law

Formulas

I = V / (R1 + R2)
R2 = V / I - R1

Theorems

Ohm's Law

Suitable Grade Level

Grades 9-12