Ohm’s Law Physics 102 Professor Lee Carkner Lecture 13

Circuit Theory  Potential difference (  V or V):   in volts (joules per coulomb)  Current (I):  I =  Q/  t  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 =  (L/A)  where  is the resistivity, L is the length, and A is the cross sectional area

Ohm’s Law  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

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  Power radiated by resistor is:  (Energy/Coulomb)(Coulomb/Second) = (Energy/Second)  V = P  Using Ohm’s law (  V = IR) we can write: P = I 2 R and P = (  V) 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  V 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  V  Since the change in potential energy is the same for each

Resistors in Series  All resistors in series have the same current (I)   Since  V eq is the sum of all the individual  V, R eq must be the sum of all of the individual R:  V eq = IR eq = IR 1 +IR 2 R eq = R 1 + R 2 + R 3 …   Note that the voltages add as well  V eq R1R1 R2R2 I

Resistors in Parallel  All resistors in parallel have the same  V   Since the current through each is I =  V/R and I eq =  V/R eq :  V/R eq =  V/R 1 +  V/R 2 1/R eq = 1/R 1 + 1/R 2 + 1/R 3...  VV R1R1 R2R2 I eq I1I1 I2I2

Next Time  Read: , 18.6, 19.7  Homework: Ch 18, P 7, 35, Ch 19, P 5, 9