 # Short Circuits

## Introduction

A circuit is said to have a short when a path in the circuit is formed that has far less resistance to the flow of current than any of the pre-existing paths between the same points. A short is often called a short circuit, even if the short constitutes only a small part of the overall circuit. Typically the resistance associated with a short circuit is so low as to be considered zero. Short circuits are most often (although not always) associated with the formation of an unintentional path of low resistance. This might be caused by an incorrect circuit design or the failure of a component. However, sometimes we may actually want to provide a low resistance path between two points and may say that we “want to short the points together.” This usually means that we want to place a wire between the points.

When there are multiple paths for current to flow, the current will divide in such a way as to minimize the overall power consumed by the circuits. (As something of an aside, the power associated with the flow of current through a resistor can be expressed in multiple ways: $VI = I^2R = V^2/R$.) If a short exists, the minimum power is achieved by having all of the current flow through the short and none of it flowing through any parallel path with non-zero resistance. Figure 1. A circuit with two parallel resistors that does not contain a short.

Figure 1 shows a circuit in which two resistors are said to be connected in parallel, meaning the same voltage appears across them). Current flowing from the (voltage) source is divided between two different branches of the circuit, designated as branch A and branch B. Branch A is the segment of the circuit that contains Resistor 1 (R1) and branch B is the segment that contains Resistor 2 (R2). There is a “law” governing the flow of current in a circuit, known as Kirchhoff's Current Law (KCL), which states that the amount of current flowing into any portion of a circuit is equal to the amount of current flowing out of that same portion of the circuit. Effectively, this law says that there is no place in the circuit where charge accumulates. From this law we know that the current flowing out of the top of the voltage source has to equal the sum of currents flowing into branches A and B. Or, more generally, the sum of all currents flowing into a wire has to equal the sum of all currents flowing out of that wire. A parallel combination of resistors, as shown in Fig. 1, is sometimes called a current divider because, although the resistors have the same voltage across them, the current is divided between the two resistors. If both resistors have equal resistance, then the current flowing through them will be equal. However, if the resistances are unequal, the currents will be unequal.

If branch B were to be “shorted,” where R2 was replaced with a wire that has no resistance, all current in the circuit would flow through branch B, and no current would flow through branch A. A short circuit has the potential to damage components as the short can expose them to currents higher than the components are rated to handle. If there is a short directly across a voltage source, this can be a dangerous situation. The reason for this is that Ohm's Law states that current through a resistor is the voltage across the resistor divided by the resistance, $I=V/R$. In the case of a short, the resistance is typically considered to be zero. Dividing a non-zero number by a value that approaches zero yields a value that approaches infinity! As you might imagine, voltage sources cannot provide infinite current and thus something is likely to break (and sparks may fly!) when a voltage source is shorted. Figure 3. Two resistors in parallel. In series with each resistor is an ammeter.

Let's consider a couple more representations of circuits: one without a short and one with a short. Similarly to Fig. 1, Fig. 3 shows a circuit that has two resistors in parallel. However, in this circuit after each resistor there is an ammeter. Ammeters are used to measure the amount of current flow and are placed in series with the branch of the circuit where current is to be measured. Ammeters are designed to have extremely low resistances so that they have minimum impact on the circuit in which they are inserted. A discussion about the use of a digital multimeter as an ammeter is available via the second box on the right.

In the circuit of Fig. 3, each resistor has 3V across it. (Again, keep in mind that the ammeters have such low resistance that they effectively behave like a wire and thus are “invisible” to the rest of the circuit.) Because the resistors each have a resistance of 10 kΩ the amount of current through each of them is 0.3mA ($3\mbox{V}/10000\Omega = 0.0003\mbox{A} = 0.3\mbox{mA}$). Figure 4. The circuit of Fig. 3 but with R1 replaced by a short.

Figure 4 depicts the same circuit as Fig. 3 but the resistor R1 has been replaced with a short. Or, thought of another way, the resistance of R1 has gone to zero. As mentioned, a strict application of Ohm's Law says that as the resistance of a branch approaches zero, for a finite voltage across the branch, the current through the branch approaches infinity. On the other hand, the amount of current through the other branch has gone to zero—all the charge wants to pass along the path of zero resistance rather than struggle through the 10 kΩ resistor.

In reality, of course, current will never reach infinity. Components in the circuit will eventually break. Please keep in mind that unintentional shorts in a circuit are the easiest way to destroy electronic components. Thus, you should be extremely mindful to avoid them!

## Important Points:

• A short is a path of no (or very low) resistance.
• A short is typically represented in a circuit diagram simply as a wire.
• We may speak of either “shorts” or “short circuits”—the two are synonymous.
• When we use the word short (or the term short circuit), we often are implying the creation of an unintentional path of low resistance.
• Unintentional shorts are the leading cause of circuit damage and one should be careful to avoid them!