Simple Parallel Circuits

The electronic components having two terminals like resistor, capacitor, inductor, diode, LED and other common devices/components can be connected with each other in different ways. The Parallel Connection is one the most common types of connections used in electronic circuits.

 

Parallel Connection in Circuits:

The two components are said to be in parallel if they are connected back to back or end to end. The potential difference or the voltage drop across each component in parallel is same and the current flowing through each component is different.

 

Example 1 of Parallel Circuit:

Let us understand from a basic circuit example where three resistors R1 (10KΩ), R2 (2KΩ) and R3 (1KΩ) are connected in parallel with each other. Now we will find out the voltage drop across each resistor, current through each resistor and total equivalent resistance of the circuit.

 Parallel Circuit

Voltage

The voltage across each component connected in parallel is the same as the source voltage. Hence

1

Where VS is the source voltage = 9V battery

2

Current:

Now applying Ohm’s Law on each resistor to find current through each one.

3

 

 

 

Hence we can draw a simple table to represent these values

R1 R2 R3
Resistance (R) 10KΩ 2KΩ 1KΩ
Voltage (V) 9V 9V 9V
Current (I) 0.9mA 4.5mA 9mA

 

 

Equivalent Resistance of the Parallel Combination of Resistors:

Rule 1:

The equivalent resistance of the parallel combination of two or more than two resistors is always less than the value of smallest resistor in parallel.

Formula for equivalent resistance of more than two resistors connected in parallel is

Rule 1

 

 

Hence we can see that the equivalent resistance (R) is less than the smallest resistance (1K) in parallel.

Rule 2:

The equivalent resistance of two equal value resistors connected in parallel is half of that resistor value.

Formula for equivalent resistance of two resistors connected in parallel is

Rule 2

 

 

The rule 1 is also applicable for two resistors

Now let R1 = R2 = R = 10KΩ

rule 2-2

 

Hence we can see that the equivalent resistance is exactly equal to half of the two resistance. We can say thatr

Rule 3:

In general, if “n” equal value resistors are connected in parallel, their equivalent resistance will be

rule 3

 

Tips:

  • Convert all the units of resistances in one single unit. The units of resistance is mΩ, Ω, KΩ, MΩ
  • For calculation do not consider the milli, Kilo, or Mega units. Simply do math on numbers and add the unit to the final result.

 

Now back to the example 1, we can draw the equivalent circuit using equivalent resistor. Now we can calculate the total current (I) flowing through the circuit。

example 1

Total Current or Equivalent Current:

Apply Ohm’s Law again

Ohm’s Law

 

We can see that this total current is the sum of all the branch currents flowing through each resistor.

Hence we can say that

 total current

Nodes:

The node is the junction point where two or more terminals meet each other.

As we can see that the connection in blue color is shared between all components in parallel.

The node 1 is positive because it is connected to DC power source positive terminal and Node 2 is negative or GND (ground) terminal because it is connected to source negative terminal.

Nodes

 

 

Rule 4:

If “n” equal resistors are connected in parallel, they will have equal current flowing through them and that current is

Current

Where  is the total / equivalent current of parallel circuit

Current Divider Rule:Current Divider Rule

The current divider rule says that the sum of all the branch currents connected in parallel is equal to the total current flowing.

Through the help of current divider rule we can find the individual branch current in Example 1.

The formula of current divider rule is

Current Divider Rule 2

Where

123

As we calculated calculated

Therefore

therefore

 

Hence it is proved from table.

 

The above discussion was in context of parallel resistor based circuits. However many other components can be connected in parallel

The parallel combination of resistors is very useful in many circuits where there is a need of a smaller resistor and you only have larger resistors available. Like if you have 2, resistors of 10K then you can make parallel combination to make it a 5K resistor. You can make it 20K also by connecting in series combination. Series combination will be discussed in later articles.

 

Other Examples of Parallel Circuit:

Parallel RLC Circuit:

The combination of various passive components like resistor, capacitor and inductor can generate different functions. The parallel RLC circuit can be used oscillator circuits, frequency tuning and filter circuits. The application of parallel RLC circuit is basically in AC high frequency circuit however the above discussed resistor RLC circuit is for DC circuit application.

 

Parallel Battery Bank:

The DC batteries can be connected in parallel combination to make a battery bank with higher AH ratings. Three 18650 batteries each 3.7V/3000mAh connected in parallel will generate an equivalent bank of 3.7V 9000mAh. Thus voltage will remain same but the capacity of battery bank will increase.

 

Parallel Connected Capacitors:

The capacitors can be connected in parallel to increase the total/equivalent capacitance. The three capacitors C1, C2 and C3 10uF each connected in parallel will make an equivalent of 30uF capacitance (C)

Parallel Connected CapacitorsParallel Connected Capacitors

Electrical Loads Connected in Parallel:

The household electrical wiring is done such that the electrical loads like Fans, Tube Lights, energy savers, Air-conditioners, Washing machines, Iron, Fridge and other appliances are connected in parallel to each other. The 220V/110VAC is supplied equally to each appliance and each appliance will draw current differently according to its wattage/power.

 

Fault in Parallel Circuits:

Open Circuit:

In Example 1, if one of the three resistors get open circuit, then the current will not flow from that resistor but the current will still flow from other two. The voltage will still be equal upon each resistor.

Short Circuit:

Similarly, if one of the three resistors get short circuit, the voltage drop across all three resistors will become zero. The current will flow at maximum from shorted resistor while the rest of the two resistors will have zero current flow.