# What's the equivalent resistance of this circuit?

This was on my physics exam today and I couldn't solve it. Switch (two red dots) was originally open, and when it was open, the capacitor is uncharged. Then the switch was closed, and they asked me to find the time constant of the charging process.

I couldn't find the time constant because I couldn't find the Req. I can not reduce this circuit any further into a simple series/parallel resistors configuration. Clearly they are neither in parallel or series with each other. So in this case, how can I calculate the time constant if Req cannot be found (the resistors are neither in parallel or in series)? Do you need differential equations to solve this? Because we haven't learned anything about that in class. (but still teach me please)

P.S. Time constant=RC Thanks...

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Maybe this goes a bit above and beyond what you were taught, but maybe that's what the exam was asking of you. If it was asking too much, then I'm sure very few got this right. You need to look at the current going through the circuit.

Look at the current going into the junction in the top middle between all the resistors (call it 2)
(V-V2)/R1-V2/R2 +(Vc-V2)/R3=0
using the constraint imposed by the junction in the top right
(V2-Vc)/R3-CdVc/dt = 0

So yeah, the way I'd solve the problem to get the time constant would be with differential equations and Kirchoff's current law (currents into a node must be zero). You could potentially use thevenin resistance or superposition, but I think KCL is the most straightforward.

gneill
Mentor
This was on my physics exam today and I couldn't solve it. Switch (two red dots) was originally open, and when it was open, the capacitor is uncharged. Then the switch was closed, and they asked me to find the time constant of the charging process.

I couldn't find the time constant because I couldn't find the Req. I can not reduce this circuit any further into a simple series/parallel resistors configuration. Clearly they are neither in parallel or series with each other. So in this case, how can I calculate the time constant if Req cannot be found (the resistors are neither in parallel or in series)? Do you need differential equations to solve this? Because we haven't learned anything about that in class. (but still teach me please)

P.S. Time constant=RC Thanks...
The way to find the time constant for the network is to "suppress" the sources, which in this case involves replacing the voltage source with a short circuit (piece of wire) and then find the resulting equivalent resistance looking into the network from where the capacitor connects: You should be able to see opportunities for simplification of the resistors. The resulting equivalent resistance will be the 'R' in the time constant.

Note that the above is part of the precess involved in finding what is called a Thevenin Equivalent Circuit for a given network.

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