# Determining current through a short circuit

Edit: So I have to calculate the current through the short circuit and what I thought of is: Applying current divider across 4kohm and then the 2kohm resistor right below to get their respective currents and then subtracting them to get the current through the short circuit. Is this method reasonable?

Edit: For the current through 4kohm resistor, applying CDR as: 2/(2+4) * 1mA = 0.33mA

I'm very new to all these concepts so any help is appreciated!

• Where have you got to so far? What do you know about current sources and voltage sources in parallel? Have you met Thevenin 's theorem, to use on R1/R2, and then again on R3/R4? Jan 20, 2021 at 15:17
• After edit: Yes, the current divider equation and KCL apply to this circuit. You can use them to find the answer. Jan 20, 2021 at 15:39
• @ElliotAlderson my calculated answer through that method is not matching my simulated circuit's values. Jan 20, 2021 at 15:45
• What did you calculate? What current flows into R1||R3? Jan 20, 2021 at 15:54
• Show how you calculated that by putting your workings into the question. Jan 20, 2021 at 16:04

Let's try a way:

You could simplify R1 and R3 as they are two resistors in parallel.

You could simplify R2 and R4 as they are two resistors in parallel.

Do you agree the circuit would overall be equivalent ? Once you do that you can calculate the voltage on the short-circuit wire.

Then, go back to the circuit with the original resistors. You have the voltage at the mid point. You can probably do it from there.

Post you final answer, we'll verify it. :-)

• I calculated the voltage at that point to be 8.69V and Isc came out as 6.97mA, is that right? Jan 20, 2021 at 15:46

Use whatever methods you feel comfortable with (node voltage, mesh current, superposition, etc.) to find the voltages across the four resistors. Use Ohm's law to find the current through the four resistors. Use KCL to find the current through the "short circuit".

Since this looks like a homework problem we won't give you the answer, but I hope these hints will get you started.

Here's how I would solve it (without numbers for obvious reasons) : -

So, start where the thick red box is and define the current as "i". Then work your way round following the red arrows to define the other currents as a ratio to "i".

Then, all you have to do is find what 3i but, first, you have to answer the purple question: -

$$\color{yellow}{\bbox[purple,5pt]{\text{what is this voltage}}}$$

And that needs you to think a little harder. Once you have that voltage, you can calculate 3i because you can parallel up R1 and R3 and add it to R2 in parallel with R4. That gives you the total loading in ohms. So, knowing what the voltage is you can calculate what 3i is.

Then you can calculate what 0.5i is.