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L04_dccircuits

# L04_dccircuits - d.c Circuits Kirchhoff's Rules There are...

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d.c. Circuits Kirchhoff'’s Rules There are two basic principles of circuitry that can be used to analyze most electrical circuits. They are called Kirchhoff’s rules. 1. Kirchhoff’s Junction rule (or current rule): The sum of the currents entering any circuit junction is equal to the sum of the currents leaving the junction. For example, if we apply the rule to the circuit in Figure 1 at the junction labeled as B, we get: I 1 = I 2 + I 3 2. Kirchhoff’s Loop rule: The sum of the changes in potential across all elements around any closed circuit loop is equal to zero, with the conventions that traversing an emf from (-) to (+) results in a positive potential change and resistors traversed in the direction of the current result in a negative potential change. For example, if we apply the rule to the circuit in Figure 1, taking the loop starting at point A and going clockwise through B, C, D and back to A, we get: - I 1 R 1 – I 3 R 3 – I 4 R 4 + E 2 + E 1 = 0 The first rule is a consequence of the conservation of charge. In a circuit, electrons cannot be created nor destroyed. If a current comes to a juncture, the total amount of electrons going into the juncture must be equal to the total number of electrons leaving the juncture. The second is a consequence of the law of conservation of energy. We have learned when dealing with gravity, that if a hiking path leads you back to the original starting point there is no net change in gravitational potential energy. Similarly in a circuit, a path that leads back to the starting point results in no in change in electrical potential energy. To easily apply Kirchhoff’s rules, it might be beneficial to label and mark currents for each of the circuit branches. You then calculate the voltage drop across each of the devices and mark which side of the device, according the current direction chosen, is at the higher electrical potential. All labels were added in red in Figure 1. Use of Meters Reminder We usually use an Ammeter to measure current and a Voltmeter to measure voltage. When drawing a schematic of a circuit, we usually label the Ammeter as “A” and the voltmeter with “V”. An example schematic is shown in Figure 2. Along with the ammeter and the voltmeter, the schematic includes 4 other devices: a power supply designated by E, and three resistors designated by R. When measuring current with an ammeter, the ammeter should be placed in series with the device we want to measure the current through. For example, as shown in the Figure, if we want to measure the current through R 1 , we place the ammeter in series with R 1 . The same current should flow through both R 1 and the ammeter.

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