Parallel Resistors

Parallel Resistors

Two resistors or any two devices are said to be in parallel when the same voltage physically appears across the two resistors

Equation of Parallel Resistors:

 

1 / R total = 1 / R1 + 1 / R2 + 1 / R3 +................

 

 

Note that we have defined the voltage across both resistor (V_p) and the current that flows through each resistor (I_a and I_b) and a voltage variable, V_p, for the voltage that appears across the parallel combination.

·    The voltage across the two resistors is the same.

·    The current through the parallel 

 combination is given by:

I_p= _Ia + I_b

Ohm's Law gives the currents through the two resistors:

I_a = V_p /R_a

I_b = V_p /R_b

We can combine all of these relations, and when we do that, we find the following.

I_p= I_a + I_b

I_p= V_p /R_a + Vp /R_b

I_p= V_p[ 1/R_a + 1/R_b]

I_p= V_p/R_parallel

Example

Find the total resistance, R_T of the following resistors connected in a parallel network.

 

The total resistance R_T across the two terminals A and B is calculated as:

 

 

 

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