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Ammeter & Voltmeter Ammeter, A, inserted into the circuit. I Voltmeter, V, across the circuit element. I 2/21/2016 1 Galvanometer = Rg Ig I g ~ 50 100 A for full scale deflection. Rg ~ 100 2/21/2016 2 Make a 1.0 Ampere full scale deflection ammeter Vg Rg I g I P RP RP Rg Ig IP Rg Ig I Ig small parallel resistor (shunt) If Rg = 100 and Ig = 50 A, then 6 6 50 10 A 50 10 A RP 100 100 0.005 6 1 A 50 10 A 1A To change the scale, change RP . 2/21/2016 3 Voltmeter Assume Rg = 100 and Ig = 50 A for full scale deflection (typical). Make a 100 V full scale deflection voltmeter. I g ( RS Rg ) V 100 V 6 RS Rg 2 10 6 50 10 A 100 negligible 2/21/2016 4 Ohmmeter 2/21/2016 5 RC Circuits 2/21/2016 6 RC Circuits • Charging a capacitor: C initially uncharged; connect switch to a at t=0 Calculate current and charge as function of time. q • Apply Kirchhoff’s Voltage Law: IR 0 C • Short term: q q0 0 0 I0 R 0 I0 R • Long term: I I 0 q 0R 0 2/21/2016 C Intermediate term: q dq R0 C dt q C 7 Solution dq q dt R RC q dq 0 / R q / RC 0 dt X / R q / RC RC q R RC t t dX dt X 0 1 dX dq RC q R RC ln x R R e 2/21/2016 t RC q R RC t ln RC R q 1 C 8 Continued Capacitive Time Constant: The greater the , the greater the charging time. RC q C (1 e t / ) dq t / I e dt R Units of : ΩF q Vc (1 e t / ) C 2/21/2016 VC C s A V C/s 9 Charging a Capacitor q C (1 e at t / ) t0 t t I R e t / at t 0 t t 2/21/2016 10 Charging a Capacitor 2/21/2016 11 RC Circuits • Discharging a capacitor: • C initially charged with Q=C • Connect switch S2 at t=0. q IR 0 • Apply Kirchhoff’s Voltage Law: C • Short term: q q0 C I0 R 0 I0 R • Long term: I I 0 Intermediate term: q dq R0 C dt q 0 R 0 2/21/2016 q 0 12 Solution q dq q R 0 dt C t dq dt C q 0 RC t q q ln q C ln RC C q C e t RC dq I e dt R 2/21/2016 t RC 13 Discharging a Capacitor q C e t RC t RC t0 t at t I at R e t0 t t 2/21/2016 14 Behavior of Capacitors • Charging – Initially, the capacitor behaves like a wire. – After a long time, the capacitor behaves like an open switch in terms of current flow. • Discharging – Initially, the capacitor behaves like a variable battery. – After a long time, the capacitor behaves like an open switch 2/21/2016 15 Magnetic Field • Large Magnetic fields are used in MRI (Nobel prize for medicine in 2003) • Extremely Large magnetic field are found in some stars • Earth has a Magnetic Field 2/21/2016 22 Bar Magnets • Bar magnet ... two poles: N and S Like poles repel; Unlike poles attract. • Magnetic Field lines: (defined in same way as electric field lines, direction and density) N S S N N N S S Attraction S 2/21/2016 N Repulsion From North to South 23 DEMO of Magnetic Field Lines Electric Field Lines of an Electric Dipole Magnetic Field Lines of a bar magnet 2/21/2016 S N 24 Magnetic Monopoles • One explanation: there exists magnetic charge, just like electric charge. An entity which carried this magnetic charge would be called a magnetic monopole (having + or - magnetic charge). • How can you isolate this magnetic charge? Try cutting a bar magnet in half: S N S N S N • In fact no attempt yet has been successful in finding magnetic monopoles in nature but scientists are looking for them. 2/21/2016 26 Earth’s Magnetic Field By convention, the N end of a bar magnet is what points at the Earth’s North Geographic Pole. Since opposite poles attract (analogous to opposite electric charges), the “North Geomagnetic Pole” is in fact a magnetic SOUTH pole, by convention. Confusing, but it’s just a convention. Just remember that we define N for bar magnets as pointing to geographic North. 2/21/2016 27 Earth’s Magnetic Field Magnetic North Pole 1999 2/21/2016 28 Earth’s Magnetic Field Magnetically Quiet Day Magnetically Disturbed Day 2/21/2016 29 Earth’s Magnetic Field Since 1904: 750 km, an average of 9.4 km per year. From 1973 to late 1983: 120 km, an average of 11.6 km per year 2/21/2016 30 Earth’s Magnetic Field