Question

How much power is dissipated by each resistor in FIGURE $EX28.8$?

Short answer

$P_1=1.92W$and$P_2=2.88W$

Step-by-step solution

Given information

We need to find the power dissipation by each resistor.

simplify

Let us consider the current flowing be $\text{'}i\text{'}$:

Then,

$$\begin{gathered} \Rightarrow i=\frac{\in }{R_1+R_2} \\ i=\frac{12V}{(12+18)\Omega } \\ I=\frac{12}{30}A \\ i=0.4A \end{gathered}$$

The power dissipated in $R_1$:

$$\begin{gathered} P_1=i^2{R}_1 \\ {P}_1={(0.4A)}^2\times 12\Omega P_1=0.16A\times 12\Omega \\ {P}_1=1.92W \end{gathered}$$

The power dissipated in $R_2$:

$$\begin{gathered} P_2=i^2{R}_2 \\ {P}_2={(0.4A)}^2\times 18\Omega P_2=16A\times 18\Omega \\ {P}_2=2.88W \end{gathered}$$

Circuit diagram