# Problem 1-12: Using Voltage Sources to Determine Node Voltages

Determine the power of $R_1, R_2$ and $Vs_1$. (Hint: there is no need to use nodal analysis; voltages between nodes can be easily found by the voltage sources.)

Solution

$V_{R_1}= Vs_1 = 10v \rightarrow P_{R_1}=\frac{V_{R_1}^2}{R_1}=50 W$

KVL around the loop shown above:
$-V_{R_{2}} -V_{R_1}+Vs_2=0 \rightarrow V_{R_2}=-14v$. Therefore, $P_{R_2}=\frac{V_{R_2}^2}{R_2}=49 W$

KCL at the node shown in the figure:
$-I_{Vs_1} +Is_1-\frac{V_{R_1}}{R_1}+\frac{V_{R_2}}{R_2}-Is_2=0$

$I_{Vs_1} =-6.5 \rightarrow P_{Vs_1}=Vs_1 \times I_{Vs_1} = -65 W$, absorbing.