Find the power dissipated in the 6Ω resistor shown in Fig.3.16.

Question

Find the power dissipated in the 6Ω resistor shown in Fig. 3.16.

Accepted Answer

First, we must find the current in the resistor by simplifying the circuit with series-parallel reductions. Thus, the circuit shown in Fig. 3.16 reduces to the one shown in Fig. 3.17. We find the current [latex]i_{o}[/latex] by using the formula for current division:

[latex]i_{o}=\frac{16}{16+4} \left(10\right) =8A [/latex].

Note that [latex]i_{o}[/latex] is the current in the [latex]1.6 \Omega[/latex] resistor in Fig. 3.16. We now can further divide [latex]i_{o}[/latex] between the [latex]6 \Omega[/latex] and[latex]4\Omega[/latex] resistors.The current in the [latex]6 \Omega[/latex] resistor is [latex]i_{6}=\frac{4}{6+4} \left(8\right) =3.2A[/latex] and the power dissipated in the [latex]6 \Omega[/latex] resistor is

[latex]p=\left(3.2\right)^{2} \left(6\right) =61.44 W[/latex] .

Question 3.3: Find the power dissipated in the 6Ω resistor shown in Fig.3....

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