Open and 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 an open circuit?

An open circuit is two isolated terminals not connected by an element of any kind, as shown in Fig. no.1. Since a path for conduction does not exist, the current associated with an open circuit must always be zero. The voltage across the open circuit, however, can be any value, as determined by the system it is connected to. In summary, therefore, In Fig. no.1(b), an open circuit exists between terminals a and b. The voltage across the open-circuit terminals is the supply voltage, but the current is zero due to the absence of a complete circuit. In a practical example provided in Fig. no.2, the excessive current demanded by the circuit caused a fuse to fail, creating an open circuit that reduced the current to zero amperes. However, it is important to note that the full applied voltage is now across the open circuit, so you must be careful when changing the fuse. If there is a main breaker ahead of the fuse, throw it first to remove the possibility of getting a shock. This situation clearly reveals the benefit of circuit breakers: You can reset the breaker without having to get near the hot wires.

What is short circuit?

A short circuit is a very low resistance, direct connection between two terminals of a network, as shown in Fig. no.3. 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 $V = IR = I(0 Ω) = 0 V$. In summary, therefore, In Fig. no.3(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. no.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. 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.