What is the Difference Between Series and Parallel Circuits?

To understand the difference between series and parallel circuits, let us first define what a circuit is.

An electric circuit is defined as a closed loop of conducting elements through which current can flow. An electric circuit basically consists of the following components:

• Voltage or a Current source
• Connecting wires
• Elements like Resistors, Capacitors, Inductors, transistors, diodes, etc.

What Makes a Circuit Series or Parallel?

A series or a parallel circuit is determined by the arrangement of the circuit elements and the flow of current in that circuit.

Series Circuit

If all the elements of a circuit are arranged in such a way that the magnitude of current that flows through each element is equal to the total current in the circuit, then the circuit is said to be a series circuit.

Series Circuit

Properties of a Series Circuit

• The same amount of current flows through each element.
• The voltage drop across each element is not the same.
• The total resistance of the circuit is the sum of the resistance of all the resistors.
• If one of the elements fails, then the current will stop flowing in the whole circuit.

Parallel Circuit

If the elements of a circuit are arranged in such a way that the magnitude of the current that flows through each element is not equal to the magnitude of the total current in the circuit, then the circuit is said to be a parallel circuit.

Parallel Circuit

Properties of a Parallel Circuit

• The total current gets divided in different proportions in all the branches of the circuit. The proportion of current in each branch is given by the ‘current divider rule’.
• The voltage drop across all the parallel elements is same.
• The total resistance of the circuit if given by the formula: 1/Total Resistance = 1/R_Branch1 + 1/_RBranch2 + …1/R_BranchN
• If any one element fails, the current stops flowing only in that particular branch of the circuit where the faulty element exists.

To say in simple words, if the current in a circuit is divided into branches then it is a parallel circuit otherwise a series circuit.

NOTE: In a series circuit if ant element stops working, then it breaks the entire circuit, whereas in case of parallel circuit if any element stops working then current won’t flow only through that particular branch. This is the reason why all the appliances on our homes are connected in parallel combination.

Differences between Series and Parallel Circuits

Criteria	Series	Parallel
Voltage Drop	Different across each element	Same across each element
Current	Same through each element	Different through each element
Resistance	Total Resistance = R1 + R2 + R3 + …. Rn	1/Total Resistance = 1/R1 + 1/R2 + …..1/Rn
Fault	If any element fails, currents stop flowing in the whole circuit	If an element fails, current stops flowing in that particular branch only.

Sample Problems

Q.1: In the following circuit diagram, determine the magnitude of current and voltage drop in each resistor.

Input Voltage = 20V, R1 = 2Ω , R2 = 4Ω , R3 = 6Ω

Answer:

In the above circuit diagram, all the resistors are connected end to end i.e. there is no branching.

Equivalent resistance

Req = R1 + R2 + R3

Req = 2 + 4 + 6 = 12Ω ┄┄┄➀

Also, V = IReq (Ohm’s law) ┄┄┄➁

From ➀ and ➁,

V = 20 = I * 12

I = 20/12 = 1.67 A

As it is a series circuit, Current through R1 = Current through R2 = Current through R3 = 1.67 A.

Let the voltage drop across R1 be V1,

V1 = I * R1

V1 = 1.67 * 2 = 3.34V

Let the voltage drop across R2 be V2,

V2 = I * R2

V2 = 1.67 * 4 = 6.68V

Let the voltage drop across R3 be V3,

V3 = I * R3

V3 = 1.67 * 6 = 10.02V

Q.2: Determine the magnitude of the current flowing through each branch of the following circuit.

Input Voltage = 20V, R1 = 2Ω , R2 = 4Ω , R3 = 6Ω

Answer:

All the resistors in the given circuit are parallel to each other, so the voltage drop across each resistor is equal.

Let the current flowing through R1 be I1 from Ohm’s law,

I1 = V/R1 = 20/2 = 10A

Let the current flowing through R2 be I2, from ohm’s law,

I2 = V/R2 = 20/4 = 5A

Let the current flowing through R1 be I1, from Ohm’s law,

I3 = V/R3 = 20/6 = 3.34A

Q.3: Find the magnitude of current and voltage drop across each resistor in the following circuit.

Input Voltage = 20V, R1 = 2Ω , R2 = 4Ω , R3 = 6Ω

Answer:

Note that the voltage drop across resistors 4Ω and 6Ω is not equal to the input voltage because of the presence of resistor 2Ω.

Finding the equivalent resistance of the circuit:

Req = R1 + (R2 || R3)

Req = R1 + [ R2*R3/(R2 + R3) ]

Req = 2 + 4*6/(4+6) = 2 + 2.4 = 4.4Ω

From Ohm’s law,

V = I * Req

I = V/Req = 20/4.4 = 4.54 A

Magnitude of current through R1 = I = 4.54 A

Voltage across R1 = I * R1 = 4.54 * 2 = 9.08Ω

As the resistors R2 and R3 are in parallel, the voltage across them is the same.

V_R2 = V_R3 = V_Total – V_R1

V_R2 = V_R3 = 20 – 9.08 = 10.92 V

Current through R2 = V_R2/R2 = 10.92/4 = 2.73 A

Current through R3 = V_R3/R3 = 10.92/6 = 1.82 A

FAQs on Series and Parallel Circuits

Q.1: Why is the voltage drop across each resistor the same in the case of a parallel resistor?

Answer:

In case of parallel circuits, the end points of each resistor is at same potential to that of the input voltage. This is the reason why potential drop across each resistor is same in case of parallel circuits.

Q.2: What is the formula for equivalent resistance in the case of series and parallel circuits?

Answer:

For a series circuit: Req = R1 + R2 + R3 + ….. + Rn For a parallel circuit: 1/Req = 1/R1 + 1/R2 +1/R3 + …… + 1/Rn

Q.3: Will the concept change if other circuit elements like capacitors and inductors are connected along with resistors?

Answer:

If Inductors and Capacitors are connected along with resistors, the behaviour of current will not change. But instead of calculating equivalent resistance, we need to calcuate the total impedance of the circuit. The following formulas are helpful: Reactance of capacitor (XC) = 1/(2fC) Reactance of inductor (XL) = 2fL Total Impedance (Z) = sqrt( R² + (XL – XC)² )