Meaning of Short and Open Circuits in Electrical

 Short and Open Circuits

When two points of circuit are connected together by a thick metallic wire (Fig. 1.38), they are said to be short-circuited. Since ‘short’ has practically zero resistance, it gives rise to two important facts : 

(i) no voltage can exist across it because V = IR = I × 0 = 0 

(ii) current through it (called short-circuit current) is very large (theoretically, infinity) Fig. 1.38 Fig. 1.39

Two points are said to be open-circuited when there is no direct connection between them (Fig. 1.39). Obviously, an ‘open’ represents a break in the continuity of the circuit. Due to this break 

 (i) resistance between the two points is infinite. 

 (ii) there is no flow of current between the two points. 

(A) Shorts’ in a Series Circuit 

Since a dead (or solid) short has almost zero resistance, it causes the problem of excessive current which, in turn, causes power dissipation to increase many times and circuit components to burn out.

 In Fig. 1.40 (a) is shown a normal series circuit 

where V = 12 V, R = R1 + R2 + R3 = 6 Ω I = V/R = 12/6 = 2 A, P = I 2 R = 22 × 6 = 24 W

 In Fig. 1.40 (b), 3-Ω resistor has been shorted out by a resistance less copper wire so that RCD = 0. 

Now, total circuit resistance R= 1 + 2 + 0 = 3 Ω. Hence, I = 12/3 = 4 A and P = 42 × 3 = 48 W. 

Fig. 1.40 (c) shows the situation where both 2 Ω and 3 Ω resistors have been shorted out of the circuit. In this case, R = 1 Ω, I = 12/1 = 12 A and P = 122 × 1 = 144 W 

Because of this excessive current (6 times the normal value), connecting wires and other circuit components can become hot enough to ignite and burn out.

(B) ‘Opens’ in a Series Circuit 

In a normal series circuit like the one shown in Fig. 1.41 (a), there exists a current flow and the voltage drops across different resistors are proportional to their resistances. If the circuit becomes ‘open’ anywhere, following two effects are produced : 

(i) since ‘open’ offers infinite resistance, circuit current becomes zero. Consequently, there is no voltage drop across R1 and R2. 

(ii) whole of the applied voltage (i.e. 100 V in this case) is felt across the ‘open’ i.e. across terminals A and B [Fig. 1.41 (b)]. 

The reason for this is that R1 and R2 become negligible as compared to the infinite resistance of the ‘open’ which has practically whole of the applied voltage dropped across it (as per Voltage Divider Rule of art. 1.15). Hence, voltmeter in Fig. 1.41 (b) will read nearly 100 V i.e. the supply voltage. 

(C) ‘Opens’ in a Parallel Circuit 

Since an ‘open’ offers infinite resistance, there would be no current in that part of the circuit where it occurs. In a parallel circuit, an ‘open’ can occur either in the main line or in any parallel branch. 

As shown in Fig. 1.42 (a), an open in the main line prevents flow of current to all branches. Hence, neither of the two bulbs glows. However, full applied voltage (i.e. 220 V in this case) is available across the open. Fig. 1.42

In this Fig. 1.42 (b), ‘open’ has occurred in branch circuits of B1. 

Since there is no current in this branch, B1 will not glow. However, as the other bulb remains connected across the voltage supply, it would keep operating normality. It may be noted that if a voltmeter is connected across the open bulb, it will read full supply voltage of 220 V.

(D) Shorts’ in Parallel Circuits 

Suppose a ‘short’ is placed across R3 (Fig. 1.43). It becomes directly connected across the battery and draws almost infinite current because not only its own resistance but that of the connecting wires AC and BD is negligible. Due to this excessive current, the wires may get hot enough to burn out unless the circuit is protected by a fuse.

Following points about the circuit of Fig. 1.43 (a) are worth noting. 

1. not only is R3 short-circuited but both R1 and R2 are also shorted out i.e. short across one branch means short across all branches. 

2. there is no current in shorted resistors. If there were three bulbs, they will not glow. 

3. the shorted components are not damaged, 

For example, if we had three bulbs in Fig. 1.43 (a), they would glow again when circuit is restored to normal conditions by removing the short-circuited. It may, however, be noted from Fig. 1.43 (b) that a short-circuit across R3 may short out R2 but not R1 since it is protected by R4.