# Behaviour of Parallel Circuits Due to Changes in Resistance

Elsewhere, discussion has ensued from multiple perspectives, as to how "appliances" connected in a parallel circuit are affected when a lower than acceptable resistance value is experienced in one branch. The circuit in question relates to a bank-fired fuel injection system, that experienced a "shorted" injector winding on one bank.

Now, from experience, real-world results of how the system may or may not function may be dependent on the engineered control strategies. When looking at a short in a coil of wire, the results may also vary based on the location of the short, so expecting a response that cannot be challenged, might be a bit of a "crapshoot" based on the variables.

However, at the core we still are still working with a basic parallel circuit. I believe the topic of parallel circuit behavior worthy of exploration, since I work with students on parallel circuits, once they have a grasp on series circuits and before we move on to series parallel circuit calculations.

There were of course a couple of clever fellows I should mention upfront, whose Laws are paramount to any discussion of electrical circuit behavior. Source: Google

Ohm's Law The potential difference (voltage) across an ideal conductor is proportional to the current through it. The constant of proportionality is called the "resistance", R. Ohm's Law is given by: V = I R where V is the potential difference between two points which include a resistance R.

Kirchhoff's current law (1st Law) states that current flowing into a node (or a junction) must be equal to current flowing out of it. This is a consequence of charge conservation. Kirchhoff's voltage law (2nd Law) states that the sum of all voltages around any closed loop in a circuit must equal zero.

The circuit of previous discussion has been determined to have a shorted injector coil, which is a "copper to copper" short, not a short to ground , which would yield different results. In other words, the distance that electrons must flow around the coil of wire that forms the magnetic solenoid winding, has been notably reduced.

What is known, is that if voltage remains the same as it does in a parallel circuit where each branch receives the same voltage potential, that if the resistance changes, current will also change inversely. In other words, if resistance goes up, current in any given branch will go down and vice versa, current will go up, if resistance is reduced.

The underlying focus though, is how any appliances will be affected in adjacent parallel branches of the circuit.

Set aside for the moment, any unusual controls that might result in variable or different results, whether we are dealing with peak and hold, saturated switch or other output control strategies. Let's just look at basic parallel circuits.

We can review and base our thoughts and circuit calculations thanks to Messrs, Ohms and Kirchhoff, who Laws that have been challenged constantly, but never disproven to date.

The accompanying parallel circuit calculations as presented in the associated figures, will have some minor result deviances, associated only due to calculator decimal placement and "ball park" rounding of the numbers used in the calculations.

The sum of all resistances in a parallel circuit will always be lower than the value for the lowest individual resistance. For this review, keeping it simple to resistance, voltage and current will be the objective.

During basic electrical diagnosis, we have students assemble various circuits to explore series, parallel and series parallel circuits. One activity has the students build a parallel circuit based on 12 volt source voltage, with three light bulbs of equal value. When the completed circuit is energized, all three bulbs illuminate with the same intensity.

When current is measured in each branch, it is equal within decimal places and given no undesired voltage drops in each branch connections or conductors, the voltage drop across each "appliance" is always the same as the applied source voltage, which when subtracted from the sum always equals zero.

However, when replacing the bulb in one branch of the parallel circuit with a simple carbon resistor, when the circuit is energized, the light bulbs in the remaining two branches "magically" no longer illuminate. How do we explain this? That seems to be an issue of contention elsewhere. We will do the math and reason why. Let's build a basic parallel circuit with three known resistance values that are different, where one significantly is lower than the other two branches. We will utilize resistors of known values in the circuit for this exercise. See Figure 1. Now for the stuff that few outside the classroom enjoy utilizing, let's apply Ohm's Law. Without giving it much conscious thought, we technicians routinely utilize the Laws as presented by Ohm and Kirchhoff when approaching electrical diagnosis.

From this, we can predict just how we expect electrical circuits will behave when influences occur on voltage, resistance or amperage. However, numbers "crunching" generally isn't something you expect to see technicians performing at the work bench with much frequency.

First, we will calculate total circuit resistance (Rt) for the parallel circuit using Ohm's Law. There are multiple ways to complete the calculations, but methods are not the focus of this activity, just the end results. So if choosing to replicate the calculations, feel free to use whichever methods you prefer. See Figure 2. You will notice that 1Rt is represented in the formula and in the subsequent steps the value 1 has been incorporated into the calculation, simply because it is easy to forget to complete the last step and end up with an incorrect result. Now that we have calculated total parallel circuit resistance, a quick check confirms that total resistance in a parallel circuit will always be lower than that of the lowest branch resistance and the result appears to support the theory. So far, so good.

Moving on, we will next use Rt to calculate total circuit amperage (It), since the sum of the branch amperages must always be equal to total circuit amperage in the parallel circuit. See Figure 3. So far, everything still appears to add up rather nicely! Next, we will calculate the total and individual branch voltage drops. Note, small discrepancies are simply a result of calculator rounding and decimal placements. When "crunching" the exact numbers manually, I assure you that each result will equal source voltage exactly. See Figure 4. All three branches drop 12 volts as expected, but only the appliance designated R1 might function based on the amperage, while R2 and R3 receive lower than required rated amperage. This is exactly how the circuit behaves when the students replace one of the three light bulbs in the parallel circuit with a resistor. The two light bulbs no longer illuminate.

FWIW, if using simple carbon resistors as "appliances", a low wattage resistor exposed to a higher than specified amperage will quickly overheat and fail, while if the resistor wattage is increased significantly, the circuit would not fail.

When drawing the circuit as a simple diagram with only a basic switch and appliances represented with fixed resistance values, we can see the effects of amperage in the parallel circuit and why an appliance with a lower resistance value will draw a higher current and possibly function, while branches now experiencing a lower than required amperage may not function in the case of the light bulbs which exhibit the 12 volt drop, but fail to illuminate.

Building a parallel circuit using three light bulbs and replacing one bulb with a resistor demonstrates the influence of changing resistance in individual branches of the parallel circuit quite nicely.

Please disregard the values in Figure 1. The resistances are correct in Figure 2

Hello Martin,

I have been involved in that "other" discussion and I appreciate your input. I have read you response here and checked out all your math but I don't think this really answers the question of the good branch injectors not working with one shorted. In your diagrams we can see that with one low resistance branch the two at 12.2 and 12.6 respectively flow .9a in round numbers.

I took the same circuit and ran the same calculations with three 12.2ohm branches. In that scenario each branch flows .98a of current, virtually the same as the circuit with one shorted branch. The only difference is the Total circuit current 6.9a vs 3a.

On it's face that makes sense because this is a parallel circuit and all branches get the same voltage so the current in each branch is controlled by the resistance of each branch. Only TOTAL current changes.

So why does the shorted injector work and the rest don't? There has to be another phenomenon going on here. My thought was that the large increase in total circuit current will cause a large voltage drop across the driver transistor thereby reducing available voltage to all the injectors. With reduced available voltage, the current in all branches will be reduced causing the good injectors to stop working. The bad injector works because it still gets enough current due to it's shorted condition.

Am I all wet here?

Hi Bob. I honestly don't know. From my perspective, if there is a short which lowers effective resistance, current increases. If the driver transistor or control tolerates higher than expected current, I think the "bad" that the injector with the short circuit would function, at least initially. From the numbers, there would be insufficient current for the good injectors to function.

I think that there are too many unknown variables involved. Exactly where the short is in the injector coil will have some influence, or control strategies built in to the driver module for current limiting? That old bank-fired system would use low resistance peak and hold type injectors and drivers.

I drew the simple parallel circuit to represent known values and a simple switch. The purpose was to illustrate why the two bulbs do not illuminate when a low resistance value is used to replace the third bulb. There is too much that we do not know about the scenario being discussed and circuit control strategies in the injector circuit being discussed.

Help me out here, I must be missing something. In your circuit you posted, R2 and R3 flow the same current regardless if R1 is 2.4 ohms or 12.2 ohms. Why would the bulbs turn off? The only difference I see is in total circuit current.

Bob, I just cited the example about the circuit that the students build. When I'm back to work in late August I will assemble the circuit and demonstrate the results of installing whatever resistor is installed in place of the third bulb. When the circuit is activated with the same source voltage, the two bulbs no longer illuminate. I will provide the voltage and actual branch current measurements for the circuit they assemble. The results are repeatable, no magic involved.

I do like the way you have approached this Martin, I am not involved or following the "other" conversation, my only critique is that I caution against referring to Kirchhoffs (Thank you for spelling it correctly BTW) voltage law (KVL) as a law, and I try not to use his "law" as a tool for electrical circuit analysis. KVL is really just a specific possibility within Faraday's Law, as Faraday's Law is just that, a law. When looking at a conservative vs a non-conservative electric field, KVL does not hold water.

Stating that the sum of the electric field around a closed path is equal to zero, is incorrect the way it is written within KVL. It is a fairly conditional law based on specific conditions that no time based changing magnetic fields are present. It holds when this condition is met and followed, when the conditions are not met Faraday's law will hold true, the sum of voltages around a loop is other than zero.

So two objects in parallel are not at the same voltage specifically when a secondary magnetic field is added that induces a time base changing secondary EMF that is not source connected to the primary measure EMF, much like the circuit in an ignition coil, or step up or down voltage transformers in hybrid inverter/converters. The voltage from point a to b depends upon the path that is taken, even in a simple parallel circuit. I had to work with these principles regularly when I was dabbling in magnetic component architecture design. When designing transformers, rf chokes, motor drive circuits, regenerative braking, etc., as long as no changing magnetic fields are present, I was good to follow KVL but all too often I could not count on it.

Hi Keith. For sure, I agree that magnetic fields offer up a variety of conditions that influence circuits in various ways. We start out with the KISS approach, exploring conductors, insulators etc, plus series, parallel and series parallel circuits.

We review the various Laws and rules from a general perspective on basic circuitry, but Ohm's Law in particular and associating calculations and predictions with measurements on circuit boards and vehicle systems is a good validation method.

We conquer the basics before adding in the potential effects of magnetic devices, which to be honest the vehicles are jam packed full of. It can be a slow process setting a good foundation on which to build.