Refer to the figure and use the principle of superposition to Find the component of the current $i$ through $R_{3}$ that is due to $V_{S 2}$.

$$\begin{aligned} & V_{S 1}=V_{S 2}=450 \mathrm{~V} \\ & R_{1}=7 \Omega \quad R_{2}=5 \Omega \\ & R_{3}=10 \Omega \quad R_{4}=R_{5}=1 \Omega \end{aligned}$$

Use the first four rules of inference to derive the conclusions of the following symbolized arguments. $1. A \supset(E \supset \sim F) \\ 2. H \vee(\sim F \supset M) \\ 3. A \\ 4 . \sim H \ / E \supset M$

Use the data of the circuit shown in the figure is a simplified $DC$ version of an $AC$ three-phase wye-wye $\mathrm{(Y-Y)}$ electrical distribution system commonly used to supply industrial loads, particularly rotating machines.

$$\begin{aligned} & V_{S 1}=V_{S 2}=V_{S 3}=170 \mathrm{~V} \\ & R_{w 1}=R_{w 2}=R_{w 3}=0.7 \Omega \\ & R_{1}=1.9 \Omega \quad R_{2}=2.3 \Omega \\ & R_{3}=11 \Omega \end{aligned}$$

a. Find the number of non-reference nodes. b. Find the number of unknown node voltages. c. Compute $v_{1}^{\prime}, v_{2}^{\prime}, v_{3}^{\prime}$, and $v_{n}^{\prime}$. Notice that once $v_{n}^{\prime}$ is known the other unknown node voltages can be computed directly by voltage division. and the figure and source transformations to Find $v_{n}^{\prime}$.

Use the data of the circuit shown in the figure is a simplified $DC$ version of an $AC$ three-phase wye-wye $\mathrm{(Y-Y)}$ electrical distribution system commonly used to supply industrial loads, particularly rotating machines.

$$\begin{aligned} & V_{S 1}=V_{S 2}=V_{S 3}=170 \mathrm{~V} \\ & R_{w 1}=R_{w 2}=R_{w 3}=0.7 \Omega \\ & R_{1}=1.9 \Omega \quad R_{2}=2.3 \Omega \\ & R_{3}=11 \Omega \end{aligned}$$

a. Find the number of non-reference nodes. b. Find the number of unknown node voltages. c. Compute $v_{1}^{\prime}, v_{2}^{\prime}, v_{3}^{\prime}$, and $v_{n}^{\prime}$. Notice that once $v_{n}^{\prime}$ is known the other unknown node voltages can be computed directly by voltage division. and the figure and the principle of superposition to Find $v_{n}^{\prime}$.

Using the data of the circuit shown in the figure is a simplified $DC$ version of an $AC$ three-phase wye-wye $\mathrm{(Y-Y)}$ electrical distribution system commonly used to supply industrial loads, particularly rotating machines.

$$\begin{aligned} & V_{S 1}=V_{S 2}=V_{S 3}=170 \mathrm{~V} \\ & R_{w 1}=R_{w 2}=R_{w 3}=0.7 \Omega \\ & R_{1}=1.9 \Omega \quad R_{2}=2.3 \Omega \\ & R_{3}=11 \Omega \end{aligned}$$

a. Find the number of non-reference nodes. b. Find the number of unknown node voltages. c. Compute $v_{1}^{\prime}, v_{2}^{\prime}, v_{3}^{\prime}$, and $v_{n}^{\prime}$. Notice that once $v_{n}^{\prime}$ is known the other unknown node voltages can be computed directly by voltage division. and the figure, a. Find the number of meshes. b. Compute the mesh currents. c. Use the mesh currents to Find $v_{n}^{f}$.

The circuit shown in the figure is a simplified $DC$ version of an $AC$ three-phase wye-wye $\mathrm{(Y-Y)}$ electrical distribution system commonly used to supply industrial loads, particularly rotating machines.

$$\begin{aligned} & V_{S 1}=V_{S 2}=V_{S 3}=170 \mathrm{~V} \\ & R_{w 1}=R_{w 2}=R_{w 3}=0.7 \Omega \\ & R_{1}=1.9 \Omega \quad R_{2}=2.3 \Omega \\ & R_{3}=11 \Omega \end{aligned}$$

a. Find the number of non-reference nodes. b. Find the number of unknown node voltages. c. Compute $v_{1}^{\prime}, v_{2}^{\prime}, v_{3}^{\prime}$, and $v_{n}^{\prime}$. Notice that once $v_{n}^{\prime}$ is known the other unknown node voltages can be computed directly by voltage division.

Use nodal analysis to find the current through $R_{4}$ in the figure. Let $R_{1}=10 \Omega, R_{2}=6 \Omega, R_{3}=4 \Omega$, $R_{4}=3 \Omega, R_{5}=2 \Omega, R_{6}=2 \Omega, I_{1}=2 \mathrm{~A}, I_{2}=3 \mathrm{~A}$, $I_{3}=5 \mathrm{~A}$.

Use mesh analysis to find the currents through every branch in the figure. Let $R_{1}=10 \Omega$, $R_{2}=5 \Omega, R_{3}=4 \Omega, R_{4}=1 \Omega, V_{1}=5 \mathrm{~V}, V_{2}=2 \mathrm{~V}$.

Use nodal analysis to find node voltages $V_{1}, V_{2}$, and $V_{3}$ in the figure. Let $R_{1}=10 \Omega, R_{2}=6 \Omega$, $R_{3}=7 \Omega, R_{4}=4 \Omega, I_{1}=2 \mathrm{~A}, I_{2}=1 \mathrm{~A}$.

Using node voltage analysis in the circuit of the figure , find the voltage $v$ across the $0.25-\Omega$ resistance.

Using node voltage analysis, find the voltages $V_{1}$ and $V_{2}$ for the circuit of the figure.

For the circuit of the figure, write the mesh equations in matrix form. Notice the form of the $[R]$.

Using mesh analysis, find the voltage $V$ across the current source in the figure.

Using mesh analysis, find the currents $I_{1}, I_{2}$, and $I_{3}$ in the circuit of the figure (assume polarity according to $I_{2}$ ).