P 3.2-3 Consider the circuit shown in Figure P 3.2-3.

 

(a) Suppose that R1 = 8 Ω and R2 = 4 Ω. Find the current i and the voltage v.

(b) Suppose, instead, that i = 2.25 A and v = 42 V. Determine the resistances R1 and R2.

(c) Suppose, instead, that the voltage source supplies 24 W of power and that the current source supplies 9 W of power. Determine the current i, the voltage v, and the resistances R1 and R2.

Figure P 3.2-3

(a) Suppose that R1 = 8 Ω and R2 = 4 Ω. Find the current i and the voltage v.

 

So the circuit looks like

The voltage across the 8 Ω resistor  must be 12 volts since it is parallel with the 12 V source.  Therefore the current through the resistor  can be found from Ohm’s law.

 

 

Now we can do a junction rule at the top of the 6 Ω resistor and

 

Solve for i

 

To get v we do a voltage walk around right loop, start at lower left and go clockwise.

 

 

Note: v3 is added because the current coming from the current source going left, so we are going through the resistor from low voltage to high voltage going clockwise.  Now solving for v

 

(b) Suppose, instead, that i = 2.25 A and v = 42 V. Determine the resistances R1 and R2.

 

The conditions given tell us that current through R1 found from the junction rule is

 

 

We know  since R1 is still in parallel with the 12 V source.  Since we know  and  we can use Ohm’s Law to get R1

 

 

We find  by doing a voltage walk again.

 

Now we can solve for R2

 

Note:  a negative resistance is possible with an active element, but not a passive element.

 

(c) Suppose, instead, that the voltage source supplies 24 W of power and that the current source supplies 9 W of power. Determine the current i, the voltage v, and the resistances R1 and R2.

If the voltage source supplies 24 W of power then the current i must be -2A in other words it goes the other way.  If the current supply is providing 9 W then v must be +3V. 

 

R1 still has 12V across it as it is still in parallel.  But the current through R1 is now 5A.

 

So we can find R1

 

We find  by doing a voltage walk again.

 

Now we can solve for R2

 

Again must be an active element.

 

Part (a)

Part (b)

Part (c)

 

 

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This page last updated on January 12, 2019