How Does Resistor Configuration Affect Circuit Resistance?

[joeeykn245]

Homework Statement

Three identical resistors are connected in parralel. The equivalent resistance increases by 700 ohm when one resistor is removed and connected in series with the remaining two, which are still in parrallel. Find resistance of each resistor

R_t1 + 700ohms = R_t2

Homework Equations

(1/R_t) = (1/R₁) + (1/R₂) ... For a parallel Circuit

R_t = R₁ + R₂ ... For a series Circuit

The Attempt at a Solution

First, we made an equation for the initial parallel circuit

RT1 +700 = RT2
1/Rt1 =1/R + 1/R +1/R
1/Rt1=3/R

1/R_t = 3/R

R = 3R_t for later substitution

RT1 +700 = RT2
1/Rt1 =1/R + 1/R +1/R
1/Rt1=3/R

For the combination circuit..

RT2 = 2/R + R


We substituted the RT1 and RT2 into R's

RT1 +700 = RT2

R/3 + 700 = R/2 + R

After plugging it in, we get 600 for R. Is this correct?

 

[Filip Larsen]

Welcome to PF!

You can easily check that yourself by inserting the R=600 ohm into your expression for the resistance of the two circuits and see if they differ by 700 ohm. But yes, 600 ohm is correct.