Problem 10-2    Source:   Problem elaborated by the author of the site.

On the circuit show in Figure 10-02.1, determine:

a) The current i_k.

b) What power is supplied and/or received by the 10 A source.

Solution of the Problem 10-2

Item a

Note that the two current sources are in parallel and in opposite directions. Therefore, they can be replaced by a single source with a value equal to the difference between them and pointing in the direction of the higher value source.

This results in a current source of 6 A pointing upwards. Moreover, it can be seen that the resistors of 4 and 6 ohms are in series resulting in an equivalent resistance of 10 ohms. See in the Figure 10-02.2 to how the circuit was. After simplifying the circuit, simply apply a current divider to calculate i_k. So:

Item b

To solve the item b we must calculate the voltage we have on the current source. As we already know the value of i_k, then applying the Ohm's law we have:

Since the voltage value is positive, this means that the positive of this voltage is on the same side as the arrow of the current source. Therefore, the current source is supplying power to the circuit. So, its power must be negative, or: