I have searched the forums and the tutorials and have not found an answer to my question. I am looking for the value of an unknown resistor, given the remaining value(s) of resistors, and the total value. I have seen derivations of the "product over sum" formula, however, I would like to use the generic "reciprocal" formula that applies to more than 2 resistors at a time.
So I'd like to solve for \(R_x\) in the standard "reciprocal" formula, where \(R_x\) represents the value of the unknown resistor, and \(R_t\) represents the total resistance of the circuit:
\(R_t=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x}}\)
I have seen the following as a derivation that solves for \(R_x\)...
\(R_x=\frac{1}{\frac{1}{R_t}-\frac{1}{R_2}-\frac{1}{R_3}\)
If this is accurate, then can someone show me the algebraic manipulation to get to it from the original?
Thanks!
So I'd like to solve for \(R_x\) in the standard "reciprocal" formula, where \(R_x\) represents the value of the unknown resistor, and \(R_t\) represents the total resistance of the circuit:
\(R_t=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_x}}\)
I have seen the following as a derivation that solves for \(R_x\)...
\(R_x=\frac{1}{\frac{1}{R_t}-\frac{1}{R_2}-\frac{1}{R_3}\)
If this is accurate, then can someone show me the algebraic manipulation to get to it from the original?
Thanks!