Help with DC circuit theory problem

I need help with this DC circuit problem: When the switch is open, voltage between points A and B is 2V. When the switch is closed, through variable resistor $R_{p}$ flows maximum current, and $R_{p}$ has the maximum power. Calculate value of resistor $R_{2}$.

Given parameters:

• $R_{1} = 100\Omega$
• $R_{3} = 200\Omega$
• $R_{4} = 400\Omega$
• $U_{ab} = 2V$ (open switch)
• $I_{pmax} = 10mA$ (closed switch)

What method to use?

Hint #1: You need to work with the Thevenin equivalent looking into nodes A and B from $R_P$.

Hint #2: What is the condition for maximum power transfer? ($R_L =\ ?$)

Hint #3: You know the total current through $R_{Th}$ and $R_P$ as well as the total voltage across both.

• How to use Thevenin theorem when parameters E,Ig,R2 are unknown? I know the condition for maximum power transfer (Rp should be equal to Rt which is Thevenins equivalent resistance), but again I don't know how to use Thevenin when there are three unknown parameters. – user300045 May 6 '15 at 6:40
• You don't need to know E or Ig. You already have the open-circuit voltage across A and B. – Adam Haun May 6 '15 at 12:38
1. as per max. power transfer current in Rp=10 mA then current in res. array should also be 10 mA...when swich is closed.
2. when swith is open the current in res. array must be 20mA being connected to constant current source.
3. current in R3-R4 should be 2/(200+400)=3.33 mA at 2V.
4. current through R1-R2 shuld be (20-3.3)=16.7 mA and voltage =100*16.7 mV=1.67 V
5. Voltage across R1 to be (2-1.67)=0.33 V
6. therefore R2=0.33/0.0167=20 ohms vtingole

comment: if voltage sourceis assumed to be in circuit and since voltage is NOT given, assume it to be zero.

7. equivqlent res. of the resistance ckt is= 2/20*10^-3=100 ohms
8. output/input impedance of voltage source=zero
9. parallel of R1 & R3=66.6 ohms
10. parallel combination of R2 & R4 =100-66.6=33.3 ohms
11. R2 should be equal to 36.36 ohms

ps; what does the polarity of voltage source indicate? I had asuumed it to be infinity as it is reverse biased. vtingole

• This is not correct -- your answer doesn't give the right current for Ipmax. You cannot assume that no current flows through the voltage source (E). – Adam Haun May 6 '15 at 17:13