Electrical – Help with ideal diode model question

I think the easiest method to solve such problems is to assume that the diodes are off (both, and then one of the two), compute the voltages across the diodes and see if there's a contradiction with your assumption. Let's call the top left diode \$D_1\$ and the diode in the middle \$D_2\$.

Case 1: \$D_1\$ off, \$D_2\$ off: Since \$D_1\$ is off there is no current through the top 5k resistor, and since \$D_2\$ is off, there is also no current through the bottom left 10k resistor. So \$V=0\$ and the voltage at the anode of \$D_1\$ is 15 Volts. Contradiction! (\$D_1\$ should be on).

Case 2: \$D_1\$ off, \$D_2\$ on: again no current through top 5k resistor. Voltage \$V\$ is

$$V=\frac{15V\cdot(5k||10k)}{10k+(5k||10k)}=3.75V$$

Contradiction! (Because the voltage across \$D_1\$ would be \$15V-3.75V=11.25V\$ and it should be on.)

Case 3: \$D_1\$ on, \$D_2\$ off: Voltage \$V\$ is

$$V=\frac{15V\cdot 10k}{5k+10k}=10V$$

The voltage at the anode of \$D_2\$ is \$15V\cdot 5k/15k=5V\$. This agrees with our assumption, because with these voltages \$D_2\$ must be off. So your solution is

$$I=0A,\quad V=10V$$

Just for the benefit of the larger audience: when you deal with purely resistive circuits containing n ideal diodes you can analyze them by guessing the state of every diode (either ON or OFF), do the calculations and then check if the results are coherent with the assumption you have made.

If you guessed right, i.e. the calculations confirm the assumption, then it can be shown that you've found the solution, which is unique. Otherwise you have to redo all the calculations changing your assumption about the state of the diodes. At worst you have to check \$2^n\$ circuit configurations (all the possible combinations of states of the n diodes), but with a bit of common sense and experience you can make the right guess with many fewer attempts.

Ok, then, but how do you check whether your assumptions are correct? Just remember what's the behavior of an ideal diode in either of its two states:

• ON state: 0 voltage drop across the diode (it's like a short circuit) and current flowing from anode to cathode.
• OFF state: 0 current flowing (it's like an open circuit) and diode is reverse biased, i.e. the voltage on the cathode is more positive than the voltage on the anode.

So, let's consider your specific circuit. If you assume both diodes are OFF, you replace them with open circuits. Then think what is the voltage at the upper leg of the resistor: since no current flows in the resistor there is no voltage drop across it... you should be able to continue from here and see that the results contradict the assumption. Hence the diodes cannot be both off.