Answer
$R_{T}$ $=$ $12$ $ohms$
$i$ $=$ $0.5$ $A$
$P_{T}$ $=$ $3$ $watts$
$v_{1}$ $=$ $3$ $volts$
$v_{2}$ $=$ $2$ $volts$
$P_{1}$ $=$ $1$ $watts$
Work Step by Step
a. equivalent resistance seen by the source
$R_{T}$ $=$ $2$ + $6$ + $4$
$R_{T}$ $=$ $12$ $ohms$
b. the current $i$
$i$ $=$ $I_{T}$ = $\frac{V}{R_{T}}$
$i$ $=$ $\frac{6}{12}$
$i$ $=$ $0.5$ $A$
c. the power delivered by the source
$P_{T}$ $=$ $I_{T}\times{V}$
$P_{T}$ $=$ $0.5\times{6}$
$P_{T}$ $=$ $3$ $watts$
d. the voltages $v_{1}$, $v_{2}$
$v_{1}$ $=$ $0.5\times{6}$
$v_{1}$ $=$ $3$ $volts$
$v_{2}$ $=$ $0.5\times{4}$
$v_{2}$ $=$ $2$ $volts$
e. the minimum power rating required for $R_{1}$
$P_{1}$ $=$ $0.5\times{2}$
$P_{1}$ $=$ $1$ $watts$
