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LAB 4: KIRCHHOFF’S RULES DIY Lab This section is adapted from reference 1. Objective In this experiment, you will experimentally verify Kirchhoff’s rules by measurement and by mathematical analysis. Apparatus (Lab Kit* or NIC Lab) 5 resistors  one 6V battery or power supply (each under 1.5 kΩ each, not all equal)  digital multimeter  12 connecting wires *If you do not have the Lab Kit, you can use equivalent items. Contact your instructor regarding equivalent items to ensure that the objective of this experiment is maintained. Introduction The most basic of electrical circuits contains a single resistor connected to the terminals of a battery. This is a complete circuit, forming a continuous path between the battery terminals. The resistor is called the load and the battery is the source of emf. We assume that all wires used as connectors are ideal, with Rwire  0 . In analyzing a circuit, we make use of a representation of the circuit termed a schematic. You are already familiar, after experiment the Basic Electric Circuits Lab, with the representation of resistors and batteries; the only new symbol we introduce is that of the node, shown in Figure 4.1 below. It is simply a point where the current divides or joins. We are now ready to analyze circuits. To analyze a circuit we do two things: 1. find the current in each component, and 2. find the potential difference across each component. The rules of circuit analysis are called Kirchhoff’s rules. The Loop Rule This rule asserts that the net change in electric potential around any closed loop in a circuit is zero. This is a statement of energy conservation, since a charge that moves around any closed DIY First-Year Physics Laboratory 

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’):

I

in

  I 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

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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...
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