Wed May 18, 2011 By: Hussain Shaikh

application of kirchhoff rule

Expert Reply
Wed May 18, 2011

1. Label + and ? for each battery. The long side of a battery
symbol is +.

2. Label the current in each branch with a symbol and an arrow.
The direction of the arrow can be chosen arbitrarily. If the current
is actually in the opposite direction, it will come out with a minus
sign in the solution.

3. Apply Kirchhoff’s junction rule at each junction and the loop
rule for each loop. You will need as many independent equations
as there are unknowns. You may write down more equations than
this, but you will find that some of the equations will be redundant
(that is, not independent in the sense of providing new
information). You may use V = i× R for each resistor, which
sometimes will reduce the number of unknowns.
4. In applying the loop rule, follow each loop in one direction only
(either clockwise or counterclockwise). Pay careful attention to
a) For a resistor, the sign of the potential difference is negative
if your chosen loop direction is the same as the chosen current
direction through that resistor; the sign is positive if you are
moving opposite to the chosen current direction.
b) For a battery, the sign of the potential difference is positive if
your loop direction moves from the negative terminal toward
the positive; the sign will be negative if you are moving from
the positive terminal toward the negative terminal.

5. Solve the equations algebraically for the unknowns. Be careful
in manipulating equations not to err with signs. At the end, check
your answer by plugging them into the original equations, or even
by using additional equations not used previously (either loop or
junction rule equation).
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