Consider the following circuit with the two resistors in parallel combination.
Using our two resistor formula above we can calculate the total circuit resistance, RT as:
One important point to remember about resistors in parallel, is that the total circuit resistance (RT) of any two resistors connected together in parallel will always be LESS than the value of the smallest resistor and in our example above RT = 14.9kΩ were as the value of the smallest resistor is only 22kΩ. Also, in the case of R1 being equal to the value of R2, ( R1 = R2 ) the total resistance of the network will be exactly half the value of one of the resistors, R/2.
Consider the two resistors in parallel above. The current that flows through each of the resistors ( IR1 and IR2 ) connected together in parallel is not necessarily the same value as it depends upon the resistive value of the resistor. However, we do know that the current that enters the circuit at point A must also exit the circuit at point B. Kirchoff's Current Laws. states that "the total current leaving a circuit is equal to that entering the circuit - no current is lost". Thus, the total current flowing in the circuit is given as:
IT = IR1 + IR2
Then by using Ohm's Law, the current flowing through each resistor can be calculated as:
Current flowing in R1 = V/R1 = 12V ÷ 22kΩ = 0.545mA
Current flowing in R2 = V/R2 = 12V ÷ 47kΩ = 0.255mA
giving us a total current IT flowing around the circuit as:
IT = 0.545mA + 0.255mA = 0.8mA or 800uA.
The equation given for calculating the total current flowing in a parallel resistor circuit which is the sum of all the individual currents added together is given as:
Itotal = I1 + I2+ I3 + ..... In
Then parallel resistor networks can also be thought of as "current dividers" because the current splits or divides between the various branches and a parallel resistor circuit having N resistive networks will have N-different current paths while maintaining a common voltage.
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