Parallel Resistors | Formula Of Parallel Resistors

I have discussed series-connected resistors, now it's time to learn more about parallel-connected resistors. First of all, I would like to recall the definition of parallel circuits.

Two components are connected in such a way that they have two common terminals. A parallel circuit is one in which all components are connected in parallel.

Similarly, two resistors are connected in parallel when they have two common terminals. It is often confusing to recognize parallel circuits. Beginners should redraw the circuits.

Properties of parallel circuits:

• Voltage remains the same in every parallel-connected resistor
• Current divides proportionally to all resistors. The larger the resistance value the less will be the current flowing through the resistor

Formula Of Parallel Resistance:

Figure 1

Let's consider the circuit in figure 1. A voltage source is in parallel with three resistors. As I discussed above, the voltage remains the same in each parallel-connected resistor. The current divides among the resistances. So, with the help of Ohm's law, we can easily evaluate the current flowing through each resistor.

Current through R1:

i1 = v/R1

Current through R2:

i2 = v/R2

Current through R3:

i3 = v/R3

The total current flowing through the circuit:

i = i1 + i2 + i3

i = v/R1 + v/R2 + v/R3

i = v{1/R1 + 1/R2 + 1/R3}

i/v = 1/R1 + 1/R2 + 1/R3

From Ohm's law i/v = 1/Req. Substitute in the above equation

1/Req = 1/R1 + 1/R2 + 1/R3

Req = R1 || R2 || R3

The easiest way to solve the above equation is the reciprocal method. Solve individual fractions first and then simply add them.

Solved Examples:

Example #1:

Determine total or equivalent resistance and the current flows through each resistor with the help of Ohm's law.

Equivalent Resistance: It is easy to solve with the help of the above formula.

1/Req = 1/R1 + 1/R2 + 1/R3

1/Req = 1/1k + 1/2k + 1/3k

Req = 545.5 Ω

Current:

Let,

i1 = current flowing through R1

i2 = current flowing through R2

i3 = current flowing through R3

Voltage remains in all three resistors as they are connected in parallel combination

.

i1 = v1/R1

i1 = 10/1000

i1 = 10mA

i2 = v1/R2

i2 = 10/2000

i2 = 5mA

i3 = v1/R3

i3 = 10/3000

i3 = 3.33mA

Conclusion:

• The total/equivalent resistance of the circuit will be less than the smallest resistance present in the parallel circuit
• If we are continuously adding parallel resistance, the total resistance of the circuit decreases
• The larger the resistance, the lower will be the current. Or you can say current will always flow through the less resistive path
• There is another simpler method of finding current through parallel resistors. This method is known as the Current Divider Rule