To rewrite the equation to express the resistance of resistor \(R_2\) in terms of \(R_\tau\) and \(R_1\), we will start with the given equation:
[tex]\[ R_2 = \frac{R_\tau - R_1}{R_\tau R_2} \][/tex]
To isolate \(R_2\), follow these steps:
1. Multiply both sides of the equation by \(R_\tau R_2\) to eliminate the denominator on the right-hand side:
[tex]\[ R_2 \cdot R_\tau R_2 = R_\tau - R_1 \][/tex]
2. This simplifies to:
[tex]\[ R_2^2 \cdot R_\tau = R_\tau - R_1 \][/tex]
3. Divide both sides of the equation by \(R_\tau\) to isolate \(R_2^2\) on the left-hand side:
[tex]\[ R_2^2 = \frac{R_\tau - R_1}{R_\tau} \][/tex]
4. Take the square root of both sides to solve for \(R_2\):
[tex]\[ R_2 = \sqrt{\frac{R_\tau - R_1}{R_\tau}} \][/tex]
Therefore, the resistance of resistor \(R_2\) in terms of \(R_\tau\) and \(R_1\) is:
[tex]\[ R_2 = \sqrt{\frac{R_\tau - R_1}{R_\tau}} \][/tex]
