A client has hired you to simplify the circuit shown in Figure, which they want to manufacture. The client is extremely tight-lipped about the purpose of the circuit, and only insists that you find a simpler equivalent circuit that will be cheaper to manufacture. At first glance you can see that the circuit is comprised of three separate voltage sources and five resistors, and you're confident you can combine some of these to make things cheaper.

The client has also given you a power supply that has three separate voltage sources: one variable source that provides anything between 0-30 V, one fixed 12 V source, and one fixed 5 V source. Straight away you can see that these sources do not match all of the sources in the circuit, but the client is expecting you can find a way to make it work! They tell you that they own a company that produces fixed 12 V and 5 V sources very cheaply, whereas variable power supplies are quite expensive. They also divulge that the 50 k? resistor in the diagram won't be a simple resistor in the final circuit, but a more complicated circuit element with the same equivalent resistance. The unknown component is rated for a minimum current of 40 ?A and a maximum current of 100 ?A.

In addition, they give you access to these resistors (all with units of ?): 25, 50, 100, 200, 220, 400, 800, 1 k, 2 k, 4 k, 5 k, 10 k, 15 k, 20 k, 30 k, 50 k, 100 k, and 1 M.

a) Using Kirchhoff's loop and junction laws, determine the current that should flow through the 50-k? resistor and also the voltage drop across it.

b) Is the current through the 50-k? resistor compatible with the client's requirements?

Hint: you have available the equipment listed below.

Resistors (all with units of?): 25, 50, 100, 200, 220, 400, 800, 1 k, 2 k, 4 k, 5 k, 10 k, 15 k, 20 k, 30 k, 50 k, 100 k, 1 M

0-30 V variable power supply, 12 V fixed power supply , 5 V fixed power supply

20 kQ +5V 50 kQ 1 kQ 4 kQ 10 kQ +4V +7V T Fig. 2: Circuit your client has hired you to simplify