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Ohm’s Law Physics 102 Professor Lee Carkner Lecture 13 Circuit Theory Potential difference (DV or V): in volts (joules per coulomb) Current (I): I = DQ/Dt in amperes (amps, coulombs per second) Resistance (R): how hard it is to get current to flow in ohms (volts per ampere) Resistance Good conductors have low resistivity, good insulators have high resitivities The total resistance of the material also depends on its size The resistance can be written as: R = r (L/A) where r is the resistivity, L is the length, and A is the cross sectional area How much current do you get if you put a potential difference V across a wire with resistance R? High voltage, low resistance means large current Commonly written as: V = IR Every individual piece of a circuit has its own value of V, I and R and obeys Ohm’s law Ohm’s Law Temperature and Resistance Resistors convert energy from the current into heat Temperature also affects electronic properties This increased random motion means collisions are more frequent and it is harder for current to flow Resistance generally increases with temperature As current flows though a resistor, its resistance changes (we usually neglect this) Energy in Electric Circuits Charges have energy: converted to converted to Power radiated by resistor is: (Energy/Coulomb)(Coulomb/Second) = (Energy/Second) IDV = P Using Ohm’s law (DV = IR) we can write: P = I2R and P = (DV)2/R Lightbulbs A common circuit element is the lightbulb Household lightbulbs are rated in watts Brightness of lightbulb = power In the US, most power outlets produce 120 volts of potential difference Those that do not use a transformer Conservation of Charge We can find V, R and I for different parts of circuit by applying two conservation rules (for charge and energy) If the current splits, the two new currents must sum to be equal to the original Otherwise charge would be gained or lost Conservation of Energy Each resistor has a DV associated with it The sum of the voltage drops across all circuit elements on a single wire must be equal to the potential difference across the ends of the wire All wires connected between the same two points must have the same DV Since the change in potential energy is the same for each Resistors in Series R1 R2 I DVeq All resistors in series have the same current (I) Since DVeq is the sum of all the individual DV, Req must be the sum of all of the individual R: DVeq = IReq = IR1 +IR2 Req = R1 + R2 + R3 … Note that the voltages add as well Resistors in Parallel R1 I1 Ieq All resistors in parallel have the same DV R2 I2 DV Since the current through each is I = DV/R and Ieq = DV/Req: DV/Req = DV/R1 + DV/R2 1/Req = 1/R1 + 1/R2 + 1/R3 ... Next Time Read: 19.1-19.4, 18.6, 19.7 Homework: Ch 18, P 7, 35, Ch 19, P 5, 9