Physics 123

19. DC Circuits 19.1 Resistors in Series and Parallel 19.6 Capacitors in Series and Parallel 19.7 RC Circuit Ammeters and Voltmeters

Bulbs in Series and Parallel A.L1 and L2 are in series B.L1 and L2 are in parallel C.L3 and L4 are in series D.None of the above L3 L4 L1L2

Bulbs in Series and Parallel L1 and L2 are in series and L3 and L4 are in parallel L3 L4 L1L2

Bulbs in Series and Parallel A.I 1 = I 2 B.V 1 = V 2 C. I 3 = I 4 D. None of the above L3 L4 L1L2

Bulbs in Series and Parallel Series Parallel I 1 = I 2 V 3 = V 4 L3 L4 L1L2

Which bulb is brighter? A.L1 and L2 are equally bright B.L1 is brighter than L2 C.L2 is brighter than L1 D.None of the above L1L2

Which bulb is brighter? None of the above. Brightness depends on power (watts) which is P = VI or P = I 2 R. In general, L1 and L2 will shine differently unless they are the same type of bulb. Different bulbs have different values of filament resistance. L1L2

Brightness of Bulbs in Parallel A.L3 and L4 are equally bright B.L3 is brighter than L4 C.L4 is brighter than L3 D.None of the above L3 L4

Brightness of Bulbs in Parallel None of the above. Brightness depends on power (watts) which is P = VI or P = V 2 / R. In general, L1 and L2 will shine differently unless they are the same type of bulb. Different bulbs have different values of filament resistance. The bulb with the smaller resistance will be brighter in this case! L3 L4

What’s wrong with this picture? In which circuit is L2 brighter? In which circuit is L1 brighter? L1L2L1L2

What’s wrong with this picture? In which circuit is L2 brighter? … Just kidding! In which circuit is L1 brighter? … Well, L1 will not light up without L2 in a series circuit. L1L2L1L2

Bulbs in Series and Parallel In which circuit is L4 brighter? In which circuit is L3 brighter? L3 L4

Bulbs in Series and Parallel In which circuit is L4 brighter? … Just kidding! In which circuit is L3 brighter? L3 will be equally bright in both circuits … And I am DEAD SERIOUS. The voltage is the same, the current is the same, the power is the same, the brightness is the same!!!! L3 L4

Comparative Brightness A.L1 and L3 are equally bright B.L3 is brighter than L1 C.L1 is brighter than L3 D.None of the above L3 L4 L1L2

Bulbs in Series and Parallel B.L3 is brighter than L1 The voltage across L3 is greater than the voltage across L1. Also, the current through L3 is greater than the current through L1 L3 L4 L1L2

Example Series Circuit Calculate the current flowing through the resistors voltage across the resistors power dissipation in the resistors R1 = 3ΩR2 = 6Ω V = 12V

Solution Series Circuit R eq = R 1 + R 2 R1 = 3ΩR2 = 6Ω V = 12V R eq = 9Ω V = 12V I = 12/9 =4/3 A V1 = 4/3 x 3 = 4 V V2 = 4/3 x 6 = 8 V

Example Parallel Circuit 12V R1 =6 Ω R2 = 3 Ω Calculate the current flowing through the resistors voltage across the resistors power dissipation in the resistors

Example Parallel Circuit 12V R1 =6 Ω R2 = 3 Ω 1/ R eq = 1/R 1 + 1/R 2 R eq =2Ω V = 12V I 1 = 12/6 =2 A I 2 = 12/3 =4 A

Example Series /Parallel Combo Special! R1 =3Ω R2 =6Ω R3 =4Ω V =12V Calculate the current flowing through the resistors voltage across the resistors power dissipation in the resistors

Solution Series /Parallel Combo Special! R1 =3Ω R2 =6Ω R3 =4Ω V =12V Req =2Ω R3 =4Ω V =12V I eq = 12/6 =2A V eq = 2 x2 = 4V V 1 = V 2 = 4V I 1 = 4/3 A and I 2 = 2/3 A

Ammeters and Voltmeters A V Ammeter measures current Ammeter is connected in series Ammeter has a LOW resistance Ammeter is tricky to hook up Voltmeter measures voltage Voltmeter is connected in parallel Voltmeter has a HIGH resistance Voltmeter is easy to hook up

Capacitors in Parallel 12V C1 =6  F C2 = 3  F C eq = C 1 + C 2 V 1 = V 2 Q 1 and Q 2 may be different

Capacitors in Series 1/C eq = 1/C 1 + 1/C 2 Q 1 = Q 2 V 1 and V 2 may be different C1 = 3  FC2 = 6  F V = 12V

RC Charging Circuit V C = V 0 (1 - e -t /RC ) V R = V 0 e -t /RC V0V0 VRVR t VCVC

RC Discharging Circuit V C = V 0 e -t /RC V R = V 0 e -t /RC VRVR t =VC=VC

That’s all folks!