question\nthe total resistance in a circuit with two parallel resistors is 2 ohms and $r_1$ is 6 ohms. using…

question\nthe total resistance in a circuit with two parallel resistors is 2 ohms and $r_1$ is 6 ohms. using the equation for $r_2$, in terms of $r_t$ and $r_1$, what is $r_2$?\n$r_2$ is ohms.

question\nthe total resistance in a circuit with two parallel resistors is 2 ohms and $r_1$ is 6 ohms. using the equation for $r_2$, in terms of $r_t$ and $r_1$, what is $r_2$?\n$r_2$ is ohms.

Answer

Explanation:

Step1: Recall parallel - resistance formula

The formula for two resistors in parallel is $\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}$.

Step2: Rearrange the formula for $R_2$

First, we get $\frac{1}{R_2}=\frac{1}{R_T}-\frac{1}{R_1}=\frac{R_1 - R_T}{R_T\times R_1}$. Then, taking the reciprocal of both sides, we have $R_2=\frac{R_T\times R_1}{R_1 - R_T}$.

Step3: Substitute the given values

Given $R_T = 2$ ohms and $R_1=6$ ohms. Substitute these values into the formula for $R_2$: $R_2=\frac{2\times6}{6 - 2}$.

Step4: Calculate the value of $R_2$

$R_2=\frac{12}{4}=3$ ohms.

Answer:

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