Short Circuits

Open circuits and short circuits can often cause more confusion and difficulty in the analysis of a system than standard series or parallel configurations.

What is short circuit?

A short circuit is a very low resistance, direct connection between two terminals of a network, as shown in Fig. 1. The current through the short circuit can be any value, as determined by the system it is connected to, but the voltage across the short circuit is always zero volts because the resistance of the short circuit is assumed to be essentially zero ohms and $V = IR = I(0 Ω) = 0 V$.
Fig. 1: Defining a short circuit.
In summary, therefore,
a short circuit can carry a current of a level determined by the external circuit, but the potential difference (voltage) across its terminals is always zero volts.
In Fig. 1(a), the current through the 2 Ω resistor is 5 A. If a short circuit should develop across the 2 Ω resistor, the total resistance of the parallel combination of the 2 Ω resistor and the short (of essentially zero ohms) will be
$$2 Ω || 0 Ω = {(2 Ω)(0 Ω) \over 2 Ω + 0 Ω} = 0 Ω$$
as indicated in [Fig .3(b)], and the current will rise to very high levels, as determined by Ohm's law:
$$I ={E \over R}= {10V \over 0Ω} = \infty A$$
The effect of the 2 Ω resistor has effectively been "shorted out" by the low-resistance connection. The maximum current is now limited only by the circuit breaker or fuse in series with the source.
Fig. 2: Demonstrating the effect of a short circuit on current levels.
For the layperson, the terminology short circuit or open circuit is usually associated with dire situations such as power loss, smoke, or fire. However, in network analysis, both can play an integral role in determining specific parameters of a system. Most often, however, if a short-circuit condition is to be established, it is accomplished with a jumper-a lead of negligible resistance to be connected between the points of interest. Establishing an open circuit just requires making sure that the terminals of interest are isolated from each other.

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