All Problems

Electric Current

Problem 3.185

Find the current flowing through the resistance R1R_{1} of the circuit shown in Fig. 3.48 if the resistances are equal to R1=10ΩR_{1}=10 \Omega, R2=20Ω,R_{2}=20 \Omega, and R3=30Ω4R_{3}=30 \Omega_{4} and the potentials of points 1,2,1,2, and 3 are equal to φ1=10 V,φ2=6 V,\varphi_{1}=10 \mathrm{~V}, \varphi_{2}=6 \mathrm{~V}, and φ3=5 V\varphi_{3}=5 \mathrm{~V}

Reveal Answer
 3.185. I1=[R3(φ1φ2)+R2(φ1φ3)]/(R1R2+R2R3++R3R1)=0.2 A\begin{array}{l} \text { 3.185. } I_{1}=\left[R_{3}\left(\varphi_{1}-\varphi_{2}\right)+R_{2}\left(\varphi_{1}-\varphi_{3}\right)\right] /\left(R_{1} R_{2}+R_{2} R_{3}+\right. \\ \left.+R_{3} R_{1}\right)=0.2 \mathrm{~A} \end{array}