CRTC Electronics

Lesson Plan

Consider the following circuit with the two resistors in parallel combination.

Using our two resistor formula above we can calculate the total circuit resistance, R_T as:

One important point to remember about resistors in parallel, is that the total circuit resistance (R_T) of any two resistors connected together in parallel will always be LESS than the value of the smallest resistor and in our example above  R_T = 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 ( I_R1 and I_R2 ) 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:

I_T = I_R1 + I_R2

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 I_T flowing around the circuit as:

I_T = 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:

I_total = I₁ + I₂+ I₃  + ..... I_n

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.