Resistors in Parallel Circuit

We have seen in earlier article about resistor connected in series connection. In this article let us study about how resistors are connected in parallel circuit. Because parallel method is most useful to consume electrical energy generated at source. Parallel which means what input given to it and same received in output. Unless special control system required most electrical loads are connected in parallel connection only. Further parallel circuit used where current control method is required in DC motor speed control system.

To connect resistors in parallel connection one end of the all resistors connected together as same as another end of those resistors are connected together. A source connected between these both junction to deliver current to it. In figure R1, R2,R3 resistors one end (A) connected which further connected with positive terminal of the source. Another end of these resistors connected together which further connected with negative terminal of the source. Using this method N number of resistors can be formed in parallel connection.

Properties of Parallel circuit

1. Total resistance or resultant resistance is equal to inverse sum of each individual resistor connected in it

Total Resistance 1/R_T = (1/R₁) +(1/R₂)+(1/R₃)+…………+1/R_n

2. Total applied voltage is equal to all resistance as individual resistors are connected across voltage

Total Voltage V_T = V₁ =V₂ = V₃ = ……….=V_n

3. Resultant current (I) delivered by source in equal to sum of all currents flowing through an individual resistance as each gets its independent path

Resultant Current I_T = I₁+I₂+I₃+………+I_n

4. Resultant resistance in parallel circuit will be less than least value of resistor connected in it
5. Current flowing though a resistor in proportional to value of it. least resistor draws more current and vice versa
6. if N number of resistors having same value connected parallel , total resistance can be determined by multiply value of single resistor with total number number of resistor connected in it
7. Total Power dissipated in circuit is equal to sum of power consumed by all individual resistors

Total Power P_T = P₁+P₂+P₃+…….+P_n

Limitations of Parallel Circuit

1. If any single resistor short circuited, then there will be abnormal increase of source current . It will damage circuit components
2. All resistor connected in circuit should able to withstand maximum magnitude of the source voltage.

Application of Parallel circuit

1. All home, commercial, industrial appliances are connected in parallel connection only
2. In DC motor speed control system rheostat are connected with field or armature winding to divert current . So speed control can be achieved
3. In Industrial electrical system power factor correction capacitors are connected in parallel with circuit.