Range of Power for Parallel Resistors
When replacing a single resistor with an equivalent pair of resistors in parallel, the total resistance of the combination will be the same as the original resistor.However, power handling capability of the new parallel combination can
differ from that of the original resistor. Consider this:
Total Resistance Calculation: For two resistors, R1 and R2, in parallel, the equivalent resistance Req is given by:
Req1=R11+R21
Power Distribution: The power dissipated in a resistor is given by P=RV2, where V is the voltage across the resistor. For the parallel combination, each resistor has same voltage across them.
Power Sharing: If P1 and P2 are the powers dissipated by resistors R1 and R2 respectively, then:
P1=R1V2andP2=R2V2
The total power dissipated by the parallel combination Ptotal is:
Ptotal=P1+P2
Power Rating of Individual Resistors: The power rating of the new resistors in parallel must be selected such that neither of them exceeds its maximum rated power. Let's suppose that the original resistor had a power rating
Poriginal.
Minimum Power Rating: The minimum power rating of each resistor in the parallel combination must be sufficient to handle its share of the total power. For equal resistors (R1=R2):
P1=P2=2Ptotal
Therefore, each resistor must have a power rating of at least 2Poriginal.
General Case: For resistors of different values, the power rating of each resistor has to be determined considering the ratio of their resistances. For resistors R1 and R2:
P1=R1+R2R2Poriginaland P2=R1+R2R1Poriginal
Example: 150 Ω and 180 Ω Resistors in Parallel
Let's analyze an example where a 150 Ω resistor is in parallel with another of 180 Ω. We will calculate the equivalent resistance and the power ratings for each resistor.
Total Resistance Calculation: For two resistors, R1=150Ω and R2=180Ω, in parallel, the equivalent resistance Req is given by:
Req1=R11+R21=1501+1801 Req1=150×180180+150=27000330 Req=33027000≈81.82Ω
Power Distribution: If the total power applied is Ptotal, the power dissipated in each resistor can be found using:
P1=R1+R2R2PtotalandP2=R1+R2R1Ptotal
Example Calculation: Consiter that the total power Ptotal is 10 W.
P1=150+180180×10W=330180×10W≈5.45W P2=150+180150×10W=330150×10W≈4.55W
Power Rating of Individual Resistors: Each resistor must have a power rating that can handle at least its share of the total power. In this example:
P1≈5.45W(for the 150 Ω resistor) P2≈4.55W(for the 180 Ω resistor)