Electric Circuits: Resistance, Ohm's Law, and Batteries - Prof. Kaustubh Agashe, Study notes of Physics

Download Electric Circuits: Resistance, Ohm's Law, and Batteries - Prof. Kaustubh Agashe and more Study notes Physics in PDF only on Docsity! Lecture 25 @ Resistance and Ohm’s law ® chapter 32 • Current created by E (requires ) related to I • resistors: circuit elements with resistance larger than wires used to limit current Resistance and Ohm’s law • R property of specific wire (depends on material and L, A): Unit of R: 1 ohm = 1 ! ! 1 V/A !V !V • E constant by current conservation E = !V!s = !V L ; I = JA; J = !E ! I = A!L!V ; R (resistance) = !L A (Resistivity: property of material only) Ohmic and Nonohmic materials; Ideal Wire Model • ideal wires: • resistors: • ideal insulators: R = 0 ! R =! " I = 0 even if !V != 0 10 to 106! !V = 0 even I != 0 • Kirchhoff’s Laws and Basic Circuit • Energy and Power • Resistors in Series Chapter 31 (Fundamentals of Circuits) • understand fundamental principles of electric circuits; direct current (DC): battery’s potential difference, currents constant • Real batteries • Resistors in Parallel Circuit Elements and Diagrams • circuit diagram: logical picture of connections (replace pictures of circuit elements by symbols) A more complex circuit • charge can flow “backwards” thru’ battery: choose cw direction for current (if solution negative, current is really ccw) • loop law: !Vbat 1 + !VR1 + !Vbat 2 + !VR2 = 0 !Vbat 1 = +E1; !Vbat 2 = !E2; !VR1 = !IR1; !VR1 = !IR2 " E1 ! IR1 ! E2 ! IR2 = 0 " I = E1!E2R1+R2 = 6 V - 9 V = 4!+2! = !0.5 A... (expected: 9 V battery “dictates” direction...) !VR1 = !IR1 = +2.0 V... Energy and Power • In battery: chemical energy potential...of charges: • power (rate at which energy supplied to charges): • In resistor: work done on charges kinetic (accelerate) between collisions thermal energy of lattice after collisions • Using Ohm’s law: Pbat = dUdt = dq dt E qEd !U = q!Vbat = qE After many collisions over length L of resistor: !Eth = qEL = q!VR rate at which energy is transferred from current to resistor: PR = dEthdt = dq dt !VR = I!VR For basic circuit: PR = Pbat (energy conservation) Echem ! U ! K ! Eth ! light... Common units: PR kW in !t hours ! PR!t kilowatt hours Resistors in Series Ammeters • current same in each resistor: • equivalent resistor: • measures current in circuit element (placed in series): !V1 = IR1; !V2 = IR2 ! !Vab = I (R1 + R2) Rab = !VabI = I(R1+R2) I = R1 + R2 Req = Rload + Rammeter ideal, Rammeter = 0 ! current not changed