Question

the electrical current in a circuit with two resistors in series can be expressed as $i=\frac{v}{r_{1}+r_{2}}$, where $v$ is the total voltage, $r_{1}$ is the resistance of the first resistor, and $r_{2}$ is the resistance of the second resistor. which shows the equation solved for the resistance of the second resistor, $r_{2}$? $r_{2}=\frac{i}{v}-r_{1}$ $r_{2}=\frac{v}{ir_{1}}$ $r_{2}=\frac{i}{v}+r_{1}$ $r_{2}=\frac{v}{i}-r_{1}$ $r_{2}=\frac{v - r_{1}}{i}$ $r_{2}=\frac{i - r_{1}}{v}$

Explanation:

Step1: Start with the given formula

Given $I=\frac{V}{R_1 + R_2}$.

Step2: Cross - multiply

$I(R_1 + R_2)=V$.

Step3: Distribute $I$

$IR_1+IR_2 = V$.

Step4: Isolate $IR_2$

$IR_2=V - IR_1$.

Step5: Solve for $R_2$

$R_2=\frac{V}{I}-R_1$.

Answer:

$R_2=\frac{V}{I}-R_1$