alternatorbridgecapacitorinductor
In a AC circuit with just a capacitor or inductor, reactance is the impedance of the component, and in a non-complex RLC circuit you can just find the total impedance with vector addition (Ztot = sqrt(R^2 + (Xl – Xc)^2), but in a complex ac circuit how do you find the impedance of a single component?
Say i want to find the impedance of components C2, C3, L2 and L3 in the circuit below.
simulate this circuit – Schematic created using CircuitLab
When a bridge is balanced, you know that there is no voltage between Va and Vb, and as a consequence, there is no current flowing between them as well. This vastly simplifies the circuit analysis, making it easy to determine the unknown component(s) relative to the known ones.
For small values of imbalance, it is possible to linearize the analysis around the balance point, which retains some of the simplicity, but for large values of imbalance, you're forced to do the full analysis of the entire circuit. It can be done, but you've given up all the advantage of using a bridge in the first place. Other circuit topologies would actually be simpler to analyze.
To simply understand the circuit you can locate a proper ground point to use as a reference for calculations and transformations of the circuit. In case of the oscilloscope, you can take one of it's connectors as the ground and split the circuit to make it easier to digest.
Given the oscillograph connections, you can transform the circuit to look like this. Does it make more sense this way?
simulate this circuit – Schematic created using CircuitLab
Try simulating it and measure the time constant from the graph, then calculate what it should be. The time constant tau is the time which it takes for the voltage to rise or fall to $$V_{initial}+(1-\frac{1}{e})\times(V_{final}-V_{initial})$$ where \$V_{initial}\$ is the stable voltage before the switching and \$V_{final}\$ is the voltage after the switching. So if before the switch it was 0 and after the switch it is 1, the time constant will be the time it took for the voltage to rise to ~0.63V.
Try replacing the capacitor with an inductive coil and see what happens in the time simulations to answer your last question thoroughly. Remember that$$ \tau = R \times C= \frac{L}{R}$$
Best Answer
These 4 elements can't be combined to find an equivalent impedance because of the presence of R2.
If you want to find the equivalent impedance of all 5 elements, including R2, you will just do the same math you would if they were all resistors, but use their complex impedance values instead of real-valued resistances.
This particular subcircuit can't be solved using just parallel and series combinations, so you'll need to either use more complex combinations like the wye-delta transform or just use KVL or KCL to form equations and solve the circuit.