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KIRCHHOFF’S RULES

Two rules, called Kirchhoff’s rules, are very useful for analysis of electric circuits.

(a) JUNCTION RULE:

• At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction.
• The proof of this rule follows from the fact that when currents are steady, there is no accumulation of charges at any junction or at any point in a line. Thus, the total current flowing in, must equal the total current flowing out.

(b) LOOP RULE:

• The algebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero .
• Since electric potential is dependent on the location of the point, thus starting with any point if we come back to the same point, the total change must be zero. In a closed loop, we do come back to the starting point and hence the rule.

In the given figure:

At junction "a" the current leaving is I₁+ I₂ and current entering is I₃. The junction rule says
I₃ = I₁+ I₂
For the loops ‘ahdcba’ and ‘ahdefga’, the loop rule gives
–30 I₁ – 41 I₃ + 45 = 0 and –30 I₁+ 21 I₂– 80 = 0.

WHEATSTONE BRIDGE

• It is an application of Kirchhoff’s rules and is a special arrangement of resistors as shown in the figure.
• There are 4 resistances R₁, R₂, R₃ and R₄ arranged in such a manner that there is a galvanometer placed between the points B and D.
• The arm BD is known as galvanometer arm. AC is known as battery arm.
• Circuit is connected to the battery across the pair of diagonally opposite points A and C.
• According to Wheatstone bridge principle:-
(R1/R2) = (R3/R4),
In such condition, the Bridge is said to be balanced.
• If the bridge is balanced there is no current flowing through the galvanometer arm.