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Resistors in parallel - (Concept)

Resistors in parallel

 

  • When two or more resistances are connected between the same two points they are said to be connected in parallel combination.

  • The figure below shows a circuit diagram where three resistors are connected in parallel combination.

               

                                                                 Figure - 7.3

 

  • IMPORTANT NOTE

    1. When a number of resistors are connected in parallel, then the potential difference across each resistance is equal to the voltage of the battery applied.

    2. When a number of resistances are connected in parallel, then the sum of the currents flowing through all the resistances is equal to total current flowing in the circuit.

    3. When numbers of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance. This happens because the same current gets additional paths to flow resulting decrease in overall resistance of the circuit

  • To calculate the equivalent resistance of the circuit shown in figure 7.3 consider a battery B which is connected across a parallel combination of resistors so as to maintain potential difference V across each resistor. Then total current in the circuit would be
                                                       

    $$
    I=I_1+I_2+I_3 \ldots
    $$


    Since potential difference across each resistors is V . Therefore, on applying Ohm's Law

    $$
    V=I_1 R_1=I_2 R_2=I_3 R_3
    $$


    $$
    I_1=\frac{V}{R_1}, I_2=\frac{V}{R_2}, I_3=\frac{V}{R_3}
    $$
     

  • For resistors connected in parallel combination reciprocal of equivalent resistance is equal to the sum of reciprocal of individual resistances.

  • Value of equivalent resistances for capacitors connected in parallel combination is always less than the value of the smallest resistance in circuit.

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JEE FOUNDATION Electricity
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