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Circuits AP Physics 1 A Basic Circuit All electric circuits have three main parts A source of energy A closed path A device which uses the energy If any part of the circuit is open the device will not work! Current Electric current is the movement of electric charges though a material. Currents are charges in motion, so we define current as the rate, in coulombs per second, at which charge moves through a wire. The unit for current is the Amp, or Ampere (A). 1 Amp = 1 Coulomb/second Kirchhoff’s Junction Law A junction is a point where a wire branches. For a junction, the law of conservation requires The basic conservation statement, that the sum of the currents into a junction equals the sum of the currents leaving, is called Kirchhoff’s junction law. Potential Difference In order to have current, we have to push our charges. In a battery, a series of chemical reactions occur in which electrons are transferred from one terminal to another. There is a potential difference (voltage) between these poles. The maximum potential difference a power source can have is called the electromotive force or (EMF), ε. The term isn't actually a force, simply the amount of energy per charge (J/C or V). The unit for potential difference is volt (V). Resistance You must continuously apply an EMF to make current flow, which means that there is something that opposes the flow of charge. We call this opposition Resistance (R). The unit for resistance is the Ohm, Ω. All materials have some resistance, even metals. The resistance of a wire is given by the equation to the right. Resistivity ρ characterizes the electrical properties of materials. Materials that are good conductors have low resistivity. Materials that are poor conductors (and thus good insulators) have high resistivity. For most circuits in this class, we will consider wires to have zero resistance (unless otherwise stated). Resistors Often, we intentionally add resistance to a circuit. In a toaster oven, we use Nichrome wire because it has a high resistivity for a metal (about 100 times more than copper). Because of this, the wires heat up and toast your bread. Resistors are used in circuits like the one below to control the amount of current and the voltages in a circuit. Voltage Drops in Circuits As current moves through a circuit, it encounters voltage drops from resistors. Each time you pass a resistor, some of the electrical energy is turned into thermal energy in the resistor. We call this a potential difference, because the potential changes as you move across the resistor. Because of this we have to measure voltage across a resistor, not at just one point. Kirchhoff’s Voltage Law Kirchhoff’s voltage law states that if you travel along any closed loop, the sum of the potential differences will be zero. Each element in the loop (battery, resistor, etc.) creates a potential difference; sometimes they will be a rise in potential, sometimes they will be a drop in potential. Ohm’s Law For most materials, increasing the amount of voltage increases the current through the material. Our constant of proportionality between these two values is the resistance of the material. This formula is referred to as Ohm’s Law. Electrical Power When current runs through a lightbulb or a resistor, it dissipates electrical energy into heat. The dissipated electrical power can be calculated using one of the following equations: The unit for power is a watt (W), just like in mechanics. Basic Circuit Components Before you begin to understand circuits you need to be able to draw what they look like using a set of standard symbols understood anywhere in the world. For the battery symbol, the long line is considered to be the positive terminal and the short line, negative. The voltmeter and ammeter are special devices you place in or around the circuit to measure the voltage and current. Ways to Wire Circuits There are 2 basic ways to wire a circuit. Keep in mind that a resistor could be anything (bulb, toaster, ceramic material…etc) Series – One after another Parallel – between a set of junctions and parallel to each other Measuring Current To determine the current in the circuit, we insert the ammeter. To do so, we must break the connection between the battery and the resistor. Because they are in series, the ammeter and the resistor have the same current. The resistance of an ideal ammeter is zero so that it can measure the current without changing the current. Measuring Voltage A voltmeter is used to measure the potential differences in a circuit. Because the potential difference is measured across a circuit element, a voltmeter is placed in parallel with the circuit element whose potential difference is to be measured. An ideal voltmeter has infinite resistance so that it can measure the voltage without changing the voltage. Because it is in parallel with the resistor, the voltmeter’s resistance must be very large so that it draws very little current. Series Circuit In a series circuit, the resistors are wired one after another. Since they are all part of the same loop they each experience the same amount of current. The sum of the voltages across each resistor is equal to the total voltage of the battery. I ( series)Total I1 I 2 I 3 V( series)Total V1 V2 V3 Equivalent Resistance in Series As the current goes through the circuit, the charges must use energy to get through the resistor. Each individual resistor will eat up some electric potential. We call this voltage drop. V( series)Total V1 V2 V3 ; V IR ( I T RT ) series I1 R1 I 2 R2 I 3 R3 Rseries R1 R2 R3 Rs Ri Example Calculate the equivalent resistance of the circuit, the current in the circuit, and the voltage drop across each resistor. Parallel Circuit In a parallel circuit, we have multiple loops. So the current splits up among the loops with the individual loop currents adding to the total current. It is important to understand that parallel circuits will all have some position where the current splits and comes back together. We call these junctions. The current going in to a junction will always equal the current going out of a junction. I ( parallel)Total I1 I 2 I 3 Regarding Junctions : I IN I OUT Equivalent Resistance in Parallel Notice that the junctions both touch the positive and negative terminals of the battery. That means you have the same potential difference down each individual branch of the parallel circuit. This means that the individual voltages drops are equal. V( parallel)Total V1 V2 V3 I ( parallel)Total I1 I 2 I 3 ; V IR VT V1 V2 V3 ( ) Parallel RT R1 R2 R3 1 1 1 1 RP R1 R2 R3 1 1 RP Ri Example Calculate the equivalent resistance of the circuit, the current in each resistor, and the voltage drop across each resistor. Complex Circuits Combinations of resistors can often be reduced to a single equivalent resistance through a step-by-step application of the series and parallel rules. Once you have found the total resistance of the circuit, you can determine the total current in the circuit. That current can be used to calculate the voltage drop across each resistor. Example Determine the current through each resistor as well as the voltage drop across each resistor. Lightbulbs Lightbulbs It is common in introductory circuits to have ranking questions for lightbulb brightness. Any time you encounter a question like this, the bulbs will be identical. Because of this, the bulb that dissipates the most power will be the brightest. Example Rank the brightness of each bulb in the circuit. Assume the bulbs are identical. Example Rank the brightness of each bulb in the circuit. Assume the bulbs are identical. Example The lightbulbs are identical. Initially both bulbs are glowing. What happens when the switch is closed? (A) Nothing. (B) A stays the same; B gets dimmer. (C) A gets brighter; B stays the same. (D) Both get dimmer. A gets brighter; (E) B goes out. Example Initially the switch in the circuit below is open. Bulbs A and B are equally bright, and bulb C is not glowing. What happens to the brightness of A and B when the switch is closed? And how does the brightness of C then compare to that of A and B? Assume that all bulbs are identical.