Shorts' in Parallel Circuits

Suppose a 'short' is placed across RJ (Fig. 1.43). ft becomes directly connected across the
ba~ery 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.
\. not only is RJ short-circuited but both Rl and R2 are also shorted out i.e. short across one
branch means short across all branches.
2. there is no current is shorted resistors. If these 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 RJ may short out R2but
not R, since it is protected by R4'
1.25. Division of Current in Parallel Circuits
In Fig. 1.44, two resistances are joined in parallel across a voltage V.
branch, as given in Ohm's law, is Hence, the division of current in the branches of a parallel
circuit is directly proportional to the conductance of the branches
or inversely proportional to their resistances. We may also
express the branch currents in terms of the total circuit current thus Equivalent Resistance ,
The equivalent resistance of a circuit (or network) between its any two points (or terminals) is
given by that single resistance which can replace the entire given circuit between these twopoints. It
should be noted that resistance is always between two given points of a circuit and can have different
values for different point-pairs as illustrated by Example 1.42. it can usually be found by using
series and parallel laws of resistances. Concept of equivalent resistance is essential for understanding
network theorems like Thevenin's theorem and Norton's theorem etc. discussed.