Physics Help Forum problem with circuit

 Sep 24th 2016, 03:47 AM #1 Junior Member   Join Date: Sep 2016 Posts: 1 problem with circuit I got a problem of this circuit diagram, where a and b are open circuit I need to find the voltage across R4 but i feel confused with finding equivalent resistance Here my way: R1 || R2 and R3 R2 is in series with R3 R2 || R4 therefore: 1/R2 + 1/R4 = 0.1= 10k ohms 10k + R3 = 10k + 20k = 30k ohms 1/10k + 1/30k = 7.5k ohms by V=IR I=4/7.5k=5.3333x10^-4 the voltage across R4=(5.33x10^-4 )(20k)=10.667V am i correct in this way since i dont have the answer
 Sep 24th 2016, 12:26 PM #2 Junior Member   Join Date: Dec 2013 Location: Encinitas, CA Posts: 18 You can't solve this circuit reducing it like that. You have to use Kirchoff's laws to solve for the currents in the circuit and the the voltage across $ab$ is the sum of the voltage across $R_3$ and the voltage across $R_4$. I would set this up as $v=(i_1-i_2)R_2 + i_1 R_4$ $0 = i_2(R_1+R_3) + (i_2-i_1)R_2$ or $\begin{pmatrix}R_2+R_4 &-R_2 \\ -R_2 &R_1+R_2+R_3 \end{pmatrix} \begin{pmatrix}i_1 \\ i_2 \end{pmatrix} = \begin{pmatrix}v \\ 0 \end{pmatrix}$ solving this you obtain $\begin{pmatrix}i_1 \\ i_2 \end{pmatrix} = \begin{pmatrix} \dfrac{v(R_1+R_2+R_3)}{R_2^2-(R_2+R_4)(R_1+R_2+R_3)} \\ \dfrac{v R_2 }{R_1 R_2 + R_1 R_4+R_2 R_3 + R_2 R_4 + R_3 R_4} \end{pmatrix}$ and $V_{ab} = i_1 R_4 + i_2 R_3 = \dfrac{v(R_1+R_2+R_3)}{R_2^2-(R_2+R_4)(R_1+R_2+R_3)}R_4 + \dfrac{v R_2 }{R_1 R_2 + R_1 R_4+R_2 R_3 + R_2 R_4 + R_3 R_4}R_3$ Attached Thumbnails   topsquark likes this. Last edited by Romsek; Sep 25th 2016 at 09:25 AM.

 Tags circuit, problem