Question

2. Use superposition to calculate the current through the 1.0kΩ resistor in the circuit shown below (show all work):

Answer 1

2.5mA

Step-by-step explanation:

The principle of superposition states that

instead of having to solve for the voltage/current through a resistor when all the power source are there, you're allowed to solve for the voltage/current through a resistor for each independent source separately and add them up in the end later for the final result.

General Step of Solving:

1. Choose which resistor you're trying to solve for.
2. Pick one of the power source and keep it on. Turn all other power sources off. Then solve for the voltage/current through the resistor of your choice.
3. Repeat step 2 for the other remaining power source.
4. Add up all the voltage/current that you found.

So.

1.) Solve for voltage through the 1k resistor when only the 15V source is on. i.e. turn off the 10V source.

2.) Solve for voltage through the 1k resistor when only the 10V source is on. i.e. turn off the 15V source.

3.) Add up the two voltage you found together.

You should get V_1k = 2.5V

so the Current through it must be I_1k = 2.5/1k = .0025A = 2.5mA