Question 2.19: Power Dissipation Figure 2.47 represents a circuit that incl...

Electrical Engineering: Concepts and Applications

Power Dissipation

Figure 2.47 represents a circuit that includes a dependent current source as detailed in Section 2.9. Here, the current of the current source is a function of the current in the 3 kΩ resistor. How much power is dissipated in the 33 kΩ resistor in Figure 2.47?

2.19

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The current source generates a current in the 33 kΩ resistor that depends on the current passing through the 3 kΩ resistor. To compute the voltage across the 33 kΩ resistor and then evaluate its power, we first find the value of $i_x$ . Using Ohm’s law, we can state:

i_x=\frac{2  V}{3  k \Omega}=667  \mu A

Therefore, $5 i_x=3.33 mA$ . Then:

v_{R}=3.33  mA \times 33  k \Omega=110  V

Next, we are able to find the value of the power dissipated in the 33 kΩ resistor. Using Equation (2.17), we see that:

$P=V \times I=\frac{V^2}{R}=R \times I^2$ (2.17)

P_{R}=110 \times 3.33 \times 10^{-3}=366.3  mW

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