Kirchhoff’s Rules path and returns to its original point must have no change in potential energy. If we apply this conservation law to a closed loop in a circuit, then
V 0 ,
where V is the potential difference across each component in the loop as measured while ‘traversing’ the loop in an arbitrary but fixed direction (i.e. either clockwise or counter clockwise). Remember, before ‘traversing’ the loop, you must assign arbitrary directions to the current in each part of the circuit. After doing so, apply the following sign conventions: 1. If you cross a cell (or battery) from the negative to the positive terminal, then this is a potential increase (or decrease if from positive to negative). 2. If you cross the resistor in the same direction as the one you assumed for the current then count the potential difference as a decrease (or increase if your direction of traversal is opposite the assumed direction of the current). To make sense of the second convention, remember: the direction of conventional current is from higher electric potential to lower electric potential. The Node Rule We also know that charge is conserved. This leads to Kirchhoff’s second rule, the node rule. The node (or junction) rule asserts that the net current into (or out of) a node is zero (i.e. ‘current in is equal to current out’):
To see these ideas in practice, consider the simple circuit in Figure 4.1:
Figure 4.1: Kirchhoff's Rules
DIY First-Year Physics Laboratory
Kirchhoff’s Rules We need to find the values of the three currents, I1, I2 and I3. Note that the presence of an emf in loop 2 ( 2 ) means that the circuit cannot be reduced to a single loop by finding a single equivalent resistance. It is in these cases that we can use Kirchhoff’s rules to set up equations containing the unknown currents. For this particular circuit, there are three unknown currents and so three equations are needed. Remember: the first step is to assume a direction for each of the unknown currents, and to label those directions on the circuit diagram. The choice of direction is arbitrary. The node rule gives us one equation: I1 I 2 I 3 Next, indicate on the circuit diagram the direction in which way you are ‘traversing’ the...