No; there is no continuous path resists light heat toasters irons bulbs 18 Ω 9 Ω three series series circuit Yes; there is still a continuous path power source parallel You could remove the 18 ohm or the 9 ohm, but not the three ohm and not both of them parallel circuit complex complex circuit series Parallel – you don’t need to turn on the coffee pot to make toast parallel complex

complex circuit 6 RT = R1 + Rp series circuit RT = 3 Ω + 6 Ω RT = R1 + R2 + R3 This parallel group is in series with the 3 Ω resistor Rcomplex = 9 Ω RT = 3 Ω + 18 Ω + 9 Ω parallel group Rseries = 30 Ω parallel circuit 1 𝑅 𝑝 = 1 𝑅 1 + 1 𝑅 2 1 𝑅 𝑇 = 1 𝑅 1 + 1 𝑅 2 + 1 𝑅 3 1 𝑅 𝑝 = 1 18 + 1 9 1 𝑅 𝑇 = 1 3 + 1 18 + 1 9 Rparallel = 2 Ω Rp = 6 Ω

12 Ω 11Ω 3 24 Ω 4 Ω 12 24 Ω 17 Ω 6 Ω 4 Ω 2 RT = 11 + 3 + 17 + 2 = 33 Ω

11 Ω 9.2 Ω 8.8 24 Ω 44 Ω 6 8 Ω 4.5 Ω 30 Ω 5 Ω 2.5 RT = 9.2 + 8.8 + 4.5 + 2.5 = 25 Ω

All resistors in series get the same current All voltages in series add All resistors in parallel get the same voltages All currents in parallel add

Which resistors get 3 amps of current? RT = 33 Ω VT = ITRT 99 = IT(33) IT = 3 amps 12 Ω 11Ω V = IR 3 V = (3)3 24 Ω 4 Ω 99 V *V = 9 V 24 Ω 17 Ω 6 Ω 4 Ω * (each resistor in this group gets 9 V) V = IR V = (3)2 *V = 6 V 2 * (each resistor in this group gets 6 V) Which resistors get 3 amps of current? The 11 ohm and the 17 ohm (and each parallel group)

R (Ω) I (amps) V (volts) P (watts) 24 6 4 17 12 11 0.25 1.5 6 0.25 6 1.5 1 6 6 1.5 6 9 3 51 153 2.25 9 20.25 6.75 0.75 9 3 33 99 P total = 297 watts

Which resistors get 2 amps of current? RT = 25 Ω VT = ITRT 50 = IT(25) IT = 2 amps 11 Ω 9.2 Ω V = IR 8.8 V = (2)8.8 24 Ω 44 Ω 50 V *V = 17.6 V 8 Ω 4.5 Ω 30 Ω 5 Ω * (each resistor in this group gets 17.6 V) V = IR V = (2)2.5 *V = 5 V 2.5 * (each resistor in this group gets 5 V) Which resistors get 2 amps of current? The 9.2 ohm and the 4.5 ohm (and each parallel group)

R (Ω) I (amps) V (volts) P (watts) 24 8 30 5 4.5 11 44 9.2 0.21 1.04 5 0.625 5 3.125 0.17 5 0.83 1 5 5 2 9 18 1.6 17.6 28.16 7.04 0.4 17.6 2 18.4 36.8 P total = 99.98 watts

R2 1Ω 9 Ω R3 R1 30 Ω 3 Ω R4 R5 R6 5 18 100 V 11 Ω 7 Ω 8 4.5 Ω R16 6 R7 5 Ω 8 Ω R10 18 Ω 3 R8 4 Ω 7.5 12 Ω R9 4 Ω R11 4 9 Ω R13 10 R12 19 Ω 11 Ω R15 R14 25 Ω 30

R1 1 ohms R2 9 ohms R3 30 ohms R4 11 ohms R5 7 ohms R6 3 ohms R7 5 ohms R8 12 ohms R9 4 ohms R10 8 ohms R11 18 ohms R12 R13 R14 R15 19 ohms R16 4.5 ohms V1 4 volts V2 20 volts V3 V4 12.2 volts V5 7.77 volts V6 12 volts V7 10 volts V8 6 volts V9 V10 16 volts V11 18 volts V12 V13 V14 11 volts V15 19 volts V16 I1 4 amps I2 2.22 amps I3 0.67 amps I4 1.11 amps I5 1.11 amp I6 I7 2 amps I8 .5 amps I9 1.5 amps I10 I11 1 amp I12 I13 3 amps I14 I15 I16 P1 16 watts P2 44.4 watts P3 13.4 watts P4 13.5 watts P5 8.63 watts P6 48 watts P7 20 watts P8 3 watts P9 9 watts P10 32 watts P11 18 watts P12 36 watts P13 P14 11 watts P15 19 watts P16 72 watts