Electrical Engineering ⇒ Topic : Parallel Circuits

Parallel Circuits

In parallel circuits, each resistance (load) is connected directly across the voltage source, as shown in Fig. (1). Thus, there are many separate paths for current flow. The voltage across all parallel branches is the same. Therefore, the current -in each branch is different and depends only on the resistance in the branch .

                                         FIGURE (1) Resistances connected in parallel

In Fig. 1 (a) two resistances R₁ and R₂ are connected in parallel. The currents through R₁ and R₂ are measured by ammeters A₁ and A₂. The total circuit current (I) is read by ammeter A. The voltage across the circuit (V) is read by voltmeter V. Applying Ohm's law, /₁ = V/R₁ and I₂ = V/R₂. If lis the total current in the circuit, then

                            ................ (1)

If R in Fig. 1 (b) represents the resistance of a single or equivalent resistor across which is applied the voltage V, and if V produces a current I through resistance R, then

                                             ............... (2)

Equations (1) and (2) represent the same current I, and therefore equating these two equations, we get

                                 .................. (3)

If the circuit consists of more than two resistors in parallel, the equivalent resistance can be expressed as

                                 ............. (4)

By applying this expression to the values given in Fig. 1 (a), we get

Reciprocal of the resistance, that is, 1/R is called conductance. The symbol commonly used for conductance is G and the unit of conductance is 'Siemens'. From Eq. (4) it follows for parallel circuits that

                                  G= G₁+ G₂ + G₃ ... + G_{n                        ................... (5)}