Basic idea of Series, Parallel and Mixed Circuit

Circuit: Circuit is a complete or closed conducting path for current where current can flow from a specific point through the circuit and can return to the same point. Practically an electrical circuit is made of one or more sources, various electrical components like resistors, capacitors inductors or many other elements interconnected by conductor where a closed loop is formed for current to flow. Look at the figure below and get a practical idea about it.

In above figure a 12V battery and 10Ω resistor are connected with wire and create a closed path, it is called circuit. Current I = 1.2A flows from battery through the circuit and return to battery.

Classification: Basically electrical circuits are classified by three categories. They are (i) Series circuit (ii) Parallel circuit and (iii) Mixed circuit.

(i) Series circuit: In series circuit there is only one conducting path to flow the current. In the following circuit two bulbs BL1 and BL2 are connected with the voltage source B1(12v) in series.

Characteristics of series circuit:

(a) A series circuit has only one conducting path.
(b) The current is same through all circuit elements.
(c) Total supply voltage is divided among all circuit elements where total voltage supplied by the source is equal to the sum of the drops across the components.
(d) In series circuit total equivalent resistance is determined by summation of all resistances. It will be cleared from example below:

In above circuit five resistors R1 to R5 are connected in series with 12V battery, where R1=6.8Ω R2=10Ω R3=1.2Ω R4=22Ω R5=100Ω. Equivalent resistance of above circuit, Req is determined by summing of these resistances.

So, Req= R1+R2+R3+R4+R5 = 6.8Ω+10Ω+1.2Ω+22Ω+100Ω = 140Ω

(e) In case of capacitor, series equivalent capacitance Ceq is determined by the formula which is described in figure below.

In above circuit three Capacitors C1 to C3 are connected in series with 12V battery, where C1=10μF C2=20μF and C3=20μF. Equivalent capacitance of above circuit, Ceq is determined by the formula written below.

(1/Ceq) = (1/C1)+(1/C2)+(1/C3)
= (1/10μF)+(1/20μF)+(1/20μF)
= 1/5μF
⇒ Ceq = 5μF

(ii) Parallel circuit: In parallel circuit there are two or more conducting paths to flow the current. In the following circuit two bulbs BL1, BL2 and a voltage source B1(12v) are connected in parallel. It has two parallel branches, one is AB branch and another is CD branch.

Characteristics of parallel circuit:

(a) A parallel circuit has two or more branches.
(b) The supply current or source current is divided through all branches where branch currents may be different to each other.
(c) Total supply voltage is same across all circuit elements.
(d) For parallel circuit total equivalent resistance is determined by a formula. It will be cleared from following example:

In above circuit three resistors R1 to R3 are connected in parallel with 12V battery, where R1=10Ω R2=20Ω R3=20Ω. Equivalent resistance of above circuit, Req is determined by the formula written below.

(1/Req) = (1/R1)+(1/R2)+(1/R3)
= (1/10Ω)+(1/20Ω)+(1/20Ω)
= 1/5Ω
⇒ Req = 5Ω

(e) For parallel circuit total equivalent capacitance is determined by summation of all capacitance. It will be cleared from example below:

In above circuit three capacitors C1 to C3 are connected in parallel with 12V battery, where C1=10μF, C2=20μF, C3=20μF. Equivalent capacitance of above circuit, Ceq is determined by summing of all these capacitances.

So, Ceq= C1+C2+C3 = 10μF+20μF+20μF = 50μF

(iii) Mixed circuit: In mixed circuit there is a combination of series and parallel circuits. Sometime mixed circuit is called series-parallel circuit.

Characteristics of mixed circuit:

(a) A mixed circuit is a combination of both series and parallel circuits.
(b) Total equivalent resistance is found from series-parallel combination of a mixed circuit.

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