Resistor Network with voltage source and current source

Question

Can i get some help on solving this circuit please? I need to calculate the output voltage Vout, but im not sure what to do when i have a current source parallel to R2.

What i tried doing is putting Vs as short circuit and dividing parallel resistor R2 by R1+R2 and multiplying by the current I1 of the current source.

Answer 1

R3 is in parallel with Vs hence it plays no part in solving the problem. Next, convert Vs and R1 to a current source: -

So now you have two current sources in parallel and the total current is the numerical sum of the individual current sources. You also have R1 and R2 both in parallel with the combined current source (easy life). So what voltage is produced by the combined current source into R1||R2?

That will be Vout.

Answer 2

Since I'm not so good with Latex sort of thing, I've solved it on paper, and am going to add a photo of it.

For given values of the resistances and voltage source, we can solve the two equations to get I1 and I2. As you can see from the solution the value of Vout can be calculated by calculating the potential difference across R2 with the mentioned polarity.

Hope this helps !

Answer 3

A quick method for this would be to create a Norton equivalent circuit. R3 is in parallel with Vs so R3 has no affect on the solution of Vo, only the total current drawn from Vs.

Vs and R2 make up your Thevenin equivalent circuit. You can convert the Vs and R2 into a current source and resistance in parallel.

^{simulate this circuit – Schematic created using CircuitLab}

Calculation is simply find the parallel resistance of R1 and R2 and use ohms law to calculate the voltage drop across the paralleled resistors where the current is the sum of I1 and your Norton current source.

OR use mesh analysis:

^{simulate this circuit}

Using mesh analysis you can calculate Vo, which is the voltage across R3.

Answer 4

Nodal analysis is, arguably, the most straightforward method in this case. Only the \$\small V_{out}\$ node is required, so, summing all currents away from that node and equating to zero:

$$\small\frac{V_{out}-V_S}{R_1}+\frac{V_{out}}{R_2}-I=0 $$ hence: $$\small V_{out} = \frac{R_2(\:V_S+IR_1)}{R_1+R_2}$$

where \$\small I=500\:\mu A\$