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Electrical Circuits An electric circuit is composed of 3 elements • Conductor, potential difference, closed loop • An electrical circuit without a load that has some resistance is essentially a short circuit •(Think about the batteries in the simulation) •(An ammeter has very little resistance. Think about my poor ammeters in a circuit with no loads or other resistance.) Electrical Circuits In a series electric circuit all of the electrons must flow through the same elements In a parallel electric circuit electrons may flow through different circuit elements Electrical Circuits In a series electric circuit, the voltage drops as it flows through each resistive circuit element Resistors in Series: Building Analogy R1 = Lamp R1 Elevator R2 = Lamp (battery) R3 = Lamp R2 3 steps To go from the top to the bottom floor, all people must take the same path. So, by definition, the staircases are in series. With each flight people lose some of the potential energy given to them by the elevator, expending all of it by the time they reach the ground floor. So the sum of the V drops across the resistors the voltage of the battery. People lose more potential energy going down longer flights of stairs, so long stairways correspond to high resistance resistors. The double waterfall is like a pair of resistors in series because there is only one route for the water to take. The longer the fall, the greater the resistance. Diagramming circuits Ohm’s Law: Ohm's Law …says that, for many materials under a wide range of conditions, the voltage, V, and current, I, are linearly related, which implies resistance, R, is independent of V and I. When does it not apply? (Most important case) Ohm’s Law Mnemonic Resistance and Ohm’s Law • Resistance is the impedance to the flow of charge • Resistance is defined as the ratio of potential difference to current • R = V/I Unit is the Ohm, Ω • A device is said to obey Ohm’s Law of its resistance is independent of the Voltage First, fill in all values of V and I. After review, fill in values of R I1 = 1 A V1 = 9 + V V2 = R2 = First, fill in all values of V and I. After review, fill in values of R I2 = A V3 = + V V4 = R4 = A I3 = 2 V V5 = 2 R5 = First, fill in all values of V and I. After review, fill in values of R I4 = 1 A V6 = + V V7 = R7 = A I5 = V V8 = 3 R8 = V9 = R9 = A I6 = V We will work this one out together I4 = A V6 = + V V7 = R7 = 1 V V7 = R7 = 2 A I5 = V V8 = 6 R8 = 3 V9 = R9 = 4 A I6 = V We will work this one out together I4 = A VT = V1 + V2 + V3 + … V V7 =3 R7 = V V8 = R8 = 2 RT = R1 + R2 + R3 + … V6 = + A I5 = IT = I1 = I2 = I3 = … V V9 = 5 R9 = V10 =4 R10 = 4 A I6 = V Questions What happens if we greatly increase the resistance? When else, besides electricity, do we see things like this? - Think about the effects on voltage (pressure), current (flow), and resistance (blockage) Tell me about heart bypassess… Tell me about heart bypassess… Parallel Circuit • More than one path for the flow of charge • More room for the flow of charge so Resistance goes down • Voltage must stay the same since all sections have the same drop Parallel Circuit: •Voltmeters are parallel to the circuit How do the sum of I1, I2, and I3 relate to IT? IT IT I2 + I3 A Hint: What is current? What is it made up of? I1 R1 IT A V V1 A A R2 R3 V V2 A V V3 Parallel Circuit: •Voltmeters are parallel to the circuit IT IT I2 + I3 A IT = I1 + I2 + I3 by Conservation of charge (conservation of matter) I1 R1 IT A V V1 R2 V V2 R3 V V3 Parallel Circuit: •Follow the current •Now map the current flow for circuit 2 IT A A R4 R1 V1, I1 R2 V2, I2 R3 R5 R6 V3, I3 IT A Circuit 1 Circuit 2 Parallel Circuit: •Follow the current •How does circuit 1 differ from circuit 2? IT A A R4 R1 IT A V1, I1 R2 V2, I2 R3 V3, I3 R5 R6 VT = 120V V1 = V2 = R1 = 100 Ohms R2 = 200 Ohms VT RT = R1 IT A IT = I1 = I2 = V1, I1 R2 V2, I2 V R1 = 100 Ohms R2 = 200 Ohms R3 = 150 Ohms VT = 120V V1 = V2 = VT RT = V3 = R1 IT A IT = I1 = I2 = I3 = V1, I1 R2 V2, I2 R3 V3, I3 V R1 = VT = 120V Rwire = 1 Ohms V1 = V2 = R2 = R3 = VT RT = V3 = R1 IT A IT = I1 = 5A (600W) I2 = 5A I3 = 5A V1, I1 R2 V2, I2 R3 V3, I3 V 1 / RT 1 / R1 1 / R2 1 / R3 ... Resistance of an object • What would we expect it to depend on? • (Resistance is the impedance to the flow of charge) Resistance of an object • What would we expect it to depend on? • (Resistance is the impedance to the flow of charge) A Find Resistance of a material • Depends on four factors – R ∞ Temp – R ∞ RHO (ρ) resitivity – R ∞ Length – R ∞ A-1 (cross-sectional Area) Low resistance • Short • Fat • cold High Resistance • Long • Thin • Hot Series and Parallel Circuits a A Resistivities at 20°C Material Resistivity Aluminum 2.82 × 10–8 Copper 1.72 × 10–8 Gold 2.44 × 10–8 Nichrome 150. × 10–8 Silver 1.59 × 10–8 Tungsten 5.60 × 10–8 From Reference tables Electrical Power • P= IV “Poison Ivy” Electrical Power • Power is the rate at which work is done or energy is expended. – Unit is Watt = Joule / second – (James Watt worked on steam engines and launched the industrial revolution) • Electrical Energy = Power * Time = VIt Electrical Power • Electrical Power is priced in kWh – One kiloWatt = 1000 Watts – One kWh = One kW for one hour Monthly Service Charge is $18 Central Hudson Variable Costs $0.047 $0.002 -$0.007 $0.004 $0.001 $0.003 $0.001 $0.004 $0.065 $0.014 Total $0.134 Monthly Charges – $6.00 Basic Charge, plus $0.06850 per Kwh for the first 600 $0.07933 per Kwh for the next 700 per Kwh for all additional $0.09260 Kwhs (Includes the effect of Schedules 59, 91, & 93) Kwhs Kwhs Example If you Kwhs of electricity, your bill would be calculated used 1450 like this: Basic Charge = $6.00 $0.06850 x 600 Kwhs = $41.100 $0.07933 $0.09260 x x 700 150 Charge for 1450 Kwhs Kwhs Kwhs = = = $55.531 $13.890 (franchise fees not $116.52included)