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Transcript
Kirchhoff’s Laws Objective: to recall Kirchhoff’s laws and use them to solve problems. Starter: what is the current and voltage in these circuits? Mark the homework Kirchhoff’s first law The German physicist Gustav Kirchhoff established two laws which help us to understand the function of electric circuits. Kirchhoff’s first law states that: The sum of the currents leaving any junction is always equal to the sum of the currents that entered it. This law is based upon the idea of the conservation of charge: no charge can be lost or made in a circuit. IIN Thus the sum of the currents at a junction should be zero. IIN = I1 + I2 … + In ΣI = 0 I1 I3 I2 Using Kirchhoff’s first law The energy in a circuit What happens to the energy supplied to a circuit? Batteries and power supplies supply electrical energy to a circuit. Devices within the circuit transduce this energy: bulbs produce heat and light, resistors produce heat. What is the conservation of energy? Energy cannot be created or destroyed. All of the energy provided by a power supply must be used by the circuit. How does the voltage of a battery relate to the voltage measured across the devices in a circuit? Voltage is the energy transferred to the charge in a circuit. The battery’s voltage is shared between the components, which transduce this energy into different forms. Kirchhoff’s second law Kirchhoff’s second law is based upon the law of the conservation of energy. It states that: The total voltage across a circuit loop is equal to the sum of the voltage drops across the devices in that loop. Essentially, the energy you put into the circuit equals the energy you get out of each circuit loop. VIN I An equation can be produced for each loop in a circuit. For example: VIN = V1 + V2 VIN = IR1 + IR2 V1 V2 R1 R2 Simple uses of Kirchhoff’s second law Further uses for Kirchhoff’s law Use Kirchhoff’s laws to find the values for each current. E = 12 V V1 10 Ω V2 100 Ω V3 40 Ω As I = V R I = 1.6 A There are 3 loops in the circuit. Each has a voltage drop equal to the input voltage according to the 2nd law. I1 Therefore: E = V1 = V2 = V3 I The 1st law means that current entering each junction equals the current leaving. I2 I3 Therefore: I= 12 10 12 + 100 I1 = 1.2 A + 12 I = I1 + I2 + I3 I = 1.2 + 0.12 + 0.3 40 I2 = 0.1 A I3 = 0.3 A Current and drift velocity Current is a flow of charge. Electrical devices activate almost instantly once they are supplied with power, however the electrons actually move around a circuit quite slowly. Their velocity is called drift velocity. Current and drift velocity are linked by the following equation: I = current (amps) I = nAve n = charged particles per unit volume A = cross-sectional area (m2) v = drift velocity (m/s) e = charge on an electron (1.6 x 10-19 C) Understanding I = nAve Alternating current and direct current RMS voltage The voltage of AC can be viewed using an oscilloscope. There are three common voltage measures, namely peak, peak-to-peak and RMS (root mean squared) voltage. peak voltage RMS voltage peak-to-peak voltage zero volts RMS is a measure of the average magnitude of the voltage. VPEAK VRMS = √2 RMS current and RMS power To investigate voltage we use an oscilloscope connected across a resistor. As V I, the equation for calculating RMS current is similar to the equation for RMS voltage: IRMS = IPEAK √2 The equation for RMS power is a little different: PPEAK = IPEAK × VPEAK PRMS = IRMS × VRMS = PPEAK PRMS = 2 IPEAK √2 VPEAK × √2 AC calculations AC/DC summary