Resistance in Series and Parallel

Tuesday 7-9-96

The relevant section in the textbook is 17.1

Main concepts:

• a series circuit is a circuit in which resistors are arranged in a chain, so that the current has only one path to take. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: R = R1 + R2 + R3 + ...

  

  A series circuit is shown in the diagram above. The current flows through each resistor in turn. If the values of the three resistors are R1 = 8 ohms, R2=8 ohms, and R3 = 4 ohms, the total resistance is 8+8+4 = 20 ohms. With a 10 V battery, by V=IR the total current in the circuit is I=V/R = 10/20 = 0.5 A. The current through each resistor would be 0.5 A.

• a parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together. The current in a parallel circuit breaks up, with parts of it flowing along each parallel branch and re-combining when the branches meet. The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total: 1/R = 1/R1 + 1/R2 + 1/R3 +...

  

  A parallel circuit is shown in the diagram above. In this case the current supplied by the battery splits up, with the amount going through each resistor depending on its resistance. If the values of the three resistors are R1 = 8 ohms, R2=8 ohms, and R3 = 4 ohms, the total resistance is found by using 1/R = 1/8 + 1/8 + 1/4 = 1/2. That gives R = 2 ohms. With a 10 V battery, by V=IR the total current in the circuit is I=V/R = 10/2 = 5 A. The individual currents can also be found using I=V/R. The voltage across each resistor is 10 V, so I1 = 10/8 = 1.25 A. I2 = 10/8 = 1.25 A. I3=10/4 = 2.5 A. Note that the currents add together to 5A, the total current.

• most circuits are made up of a combination of series and parallel resistors. Generally, the total resistance in a circuit like this is found by reducing the different series and parallel combinations step-by-step to end up with a single equivalent resistance for the circuit. This allows the current to be determined easily. The current flowing through each resistor can then be found by undoing the reduction process.

  Relevant demonstrations for this session include:

  • Electrical equivalent of heat
  • Series and parallel light bulbs