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Electric Current

Problem 3.185

Find the current flowing through the resistance \(R_{1}\) of the circuit shown in Fig. 3.48 if the resistances are equal to \(R_{1}=10 \Omega\), \(R_{2}=20 \Omega,\) and \(R_{3}=30 \Omega_{4}\) and the potentials of points \(1,2,\) and 3 are equal to \(\varphi_{1}=10 \mathrm{~V}, \varphi_{2}=6 \mathrm{~V},\) and \(\varphi_{3}=5 \mathrm{~V}\)

Reveal Answer
 3.185. I1=[R3(φ1−φ2)+R2(φ1−φ3)]/(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}
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