Theoretical Parallel Circuits

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In a parallel circuit the components are connected to the power source so that the same voltage is applied to all of the components at the same time.

In the diagram opposite, when Sw1 is closed a 12 volt battery applies a voltage to the two parallel lamps Lp1 and Lp2.

When the current flows from the battery and through Sw1 it splits and runs through both Lp1 and Lp2.

Lp1 and Lp2 being identical, have the same resistance (24 Ohms).Under these circumstances the current though each lamp will be the same (exactly half of the total current flow through the circuit).

Simple parallel Circuit

Fig 8


Current flowing through a parallel circut splits into smaller flows with a reduced current flow through each of the branches. When the current exits the branch it recombines forming a single flow equal to the input current.

Ohms Law is used to find the current flow through the circuit.
First you will need to know the total resistance for the circuit. Using the formula for parallel resistance circuits:-
  • 1/Rt= 1/R1 + 1/R2 ...
  • 1/Rt= 1/Lp1 + 1/Lp2
  • 1/Rt= 1/24 + 1/24
  • 1/Rt= 2/24
  • Answer = 12 Ohms

You had probably worked this out in your mind since the two lamps were identical and when placed in parallel the total resistance would be halved.

As a rule thumb when working out parallel resistances, remember the total resistance you expect to find must be less than the smallest individual resistance in the parallel circuit.

Total current flow

The total current flowing through the circuit can be found from Ohms Law: -

    I = V/R

    = 12/12
    = 1 Amp
To find the current flow through the individual lamps again use Ohms Law:

    I = V/R

    = 12/24
    = 0.5 Amps

Again you should have known in such a simple circuit what the value would be without the use of calculation.

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