Problem

For the circuit shown in Fig. 2.45, find: (a) v1and v2,(b) the power dissipated in the 3-k...

For the circuit shown in Fig. 2.45, find: (a) v1and v2,(b) the power dissipated in the 3-kfl and 20-kfl resistors, and (c) the power supplied by the current source.

Answer:(a) 15V, 20V, (b) 75 mW, 20 mW, (c) 200 mW.

Step-by-Step Solution

Solution 1

Refer to Figure 2.77 in the textbook.

Redraw the circuit with node notations, as shown in Figure 1.

Picture 3

Apply Kirchhoff's current law at node \(d\).

$$ \begin{aligned} &2-I_{4}-4=0 \\ &I_{4}=-4+2 \\ &=-2 \mathrm{~A} \end{aligned} $$

Hence, the current \(I_{4}\) is, \(-2 \mathrm{~A}\).

Apply Kirchhoff's current law at node \(c\).

$$ I_{4}-I_{3}+7=0 $$

Substitute \(-2\) for \(I_{4}\).

$$ \begin{aligned} &-2-I_{3}+7=0 \\ &I_{3}=5 \mathrm{~A} \end{aligned} $$

Hence, the current \(I_{3}\) is, \(5 \mathrm{~A}\).

Apply Kirchhoff's current law at node \(b\).

$$ \begin{aligned} &-3-I_{2}-7=0 \\ &I_{2}=-10 \mathrm{~A} \end{aligned} $$

Hence, the current \(I_{2}\) is, \(-10 \mathrm{~A}\).

Apply Kirchhoff's current law at node a.

$$ I_{1}+I_{2}-2=0 $$

Substitute \(-10\) for \(I_{2}\)

$$ \begin{aligned} &I_{1}-10-2=0 \\ &I_{1}=12 \mathrm{~A} \end{aligned} $$

Hence, the current \(I_{1}\) is, \(12 \mathrm{~A}\).

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