I have discussed series connected resistor , it is time to learn more about parallel connected resistor. First I would like to mention the definition of parallel circuits.
Two components are connected in such a way that they have two common connections. A parallel circuit is a circuit in which all components are connected in parallel.
Similarly, two resistors are connected in parallel if they have two common terminals. It is often confusing to identify parallel circuits. Beginners will have to redesign the circuits.
Properties of parallel circuits:
- The voltage remains the same across each resistor connected in parallel.
- The current is divided proportionally between all the resistors. The higher the value of the resistor, the less current will flow through the resistor.
Formula for parallel forces:
illustration 1
Consider the circuit in Figure 1. A voltage source is connected in parallel with three resistors. As I explained earlier, the voltage of each resistor connected in parallel remains the same. The current is divided between the resistors. Therefore, using Ohm's law, we can easily calculate 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 in 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
According to Ohm's law, i/v = 1/Req. Substitute into the above equation
1 / Required = 1 / R1 + 1 / R2 + 1 / R3
Request = R1 || R2 || R3
The easiest way to solve the above equation is the reciprocal method. First solve the individual fractions and then add them.
Worked examples:
Example 1:
Determine the total or equivalent resistance and the current per resistor using Ohm's law.
Equivalent resistance: It is easy to solve with the previous formula.
1 / Required = 1 / R1 + 1 / R2 + 1 / R3
1 / Required = 1 / 1k + 1 / 2k + 1 / 3k
Required = 545.5 Ω
Operation:
leave it
i1 = current through R1
i2 = current through R2
i3 = current through R3
The voltage remains across the three resistors because they are connected in parallel.
.
i1 = v1 / R1
i1 = 10/1000
i1 = 10mA
i2 = v1 / R2
i2 = 10/2000
i2 = 5mA
i3 = v1 / R3
i3 = 10/3000
i3 = 3.33 mA
Conclusion:
- The total/equivalent resistance of the circuit is less than the minimum resistance in the parallel circuit
- If we continuously add resistance in parallel, the total resistance of the circuit will decrease
- The higher the resistance, the lower the current. Or you could say that current always follows the path of least resistance.
- There is another simpler method to find the current through resistors in parallel. This method is known as the current divisor rule .