Resistors in Series and Parallel Circuits Resistors in

Resistors in Series and Parallel Circuits

Resistors in circuits n To determine the current or voltage in a circuit that contains multiple resistors, the total resistance must first be calculated. n Resistors can be combined in series or parallel.

Resistors in Series n When connected in series, the total resistance (Rt) is equal to: Rt = R 1 + R 2 + R 3 +… n The total resistance is always larger than any individual

Sample Problem Calculate the total current through the circuit. 15 Ω 10 Ω 6Ω Rt = I = V/Rt = 10 V

Sample Problem Calculate the total current through the circuit. 15 Ω 10 Ω 6Ω Rt = 15 Ω +10 Ω + 6 Ω Rt = I = V/Rt 10 V

Sample Problem Calculate the total current through the circuit. 15 Ω 10 Ω 6Ω Rt = 15 Ω +10 Ω + 6 Ω Rt = 31 Ω I = V/Rt = 10 V/ 31 Ω = 10 V

Sample Problem Calculate the total current through the circuit. 15 Ω 10 Ω 6Ω Rt = 15 Ω +10 Ω + 6 Ω Rt = 31 Ω I = V/Rt = 10 V/ 31 Ω = 0. 32 A 10 V

Resistors in Series n Since charge has only one path to flow through, the current that passes through each resistor is the same. n The sum of all potential differences equals the potential difference across the battery. 5 V 3 V 2 V 10 V

Resistors in Parallel n When connected in parallel, the total resistance (Rt) is equal to: 1/Rt = 1/R 1 + 1/R 2 + 1/R 3 +… n Due to this reciprocal relationship, the total resistance is always smaller than any individual resistance.

Sample Problem Calculate the total resistance through this segment of a circuit. 12 Ω 4Ω 1/Rt = = 6Ω 1/Rt =

Sample Problem Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω 12 Ω 4Ω = 6Ω 1/Rt =

Sample Problem Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω 12 Ω 4Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω 6Ω 1/Rt =

Sample Problem Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω 12 Ω 4Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω 1/Rt = 6/12 Ω = ½ Ω Rt = 6Ω

Sample Problem Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω 12 Ω 4Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω 1/Rt = 6/12 Ω = ½ Ω Rt = 2 Ω 6Ω

Resistors in Parallel n Since there is more than one possible path, the current divides itself according to the resistance of each path. smallest resistor = more current passes largest resistor = least current passes

Resistors in Parallel n The voltage across each resistor in a parallel combination is the same. 10 V

Calculate the total resistance in the circuit below 3Ω 2Ω 6Ω 4Ω Rtot = + 1/Rtot = -

Calculate the total resistance in the circuit below 3Ω 2Ω 6Ω 4Ω Rtot = 3 Ω + 2 Ω = 5 Ω Rtot = 6 Ω + 4 Ω = 10 Ω Rtot = + 1/Rtot = -

Calculate the total resistance in the circuit below 3Ω 2Ω 6Ω 4Ω Rtot = 3 Ω + 2 Ω = 5 Ω Rtot = 6 Ω + 4 Ω = 10 Ω Rtot = + - 1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω

Calculate the total resistance in the circuit below 3Ω 2Ω 6Ω 4Ω Rtot = 3 Ω + 2 Ω = 5 Ω Rtot = 6 Ω + 4 Ω = 10 Ω Rtot = 3 + - 1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω 1/3 Ω