Increment value of equvalent resistance when the resistances are parallel

In summary, the conversation discusses two resistances in parallel, their increments in resistance, and the equivalent resistance. It also mentions the value of the change in equivalent resistance over the equivalent resistance. The discussion also touches on the function R3 and its total differential/change. Finally, a specific equation is mentioned and the process of deriving it is requested.
  • #1
sudhir1962
4
0
R1 & R2 are two resistances in parallel. d(R1) & d(R2) are the incremnet in resistance. If R3 is the equvalent resisitance such that R3=R1*R2/R1+R2, then if d(R3) is increment in equvalent resistance. What is the value of d(R3)/R3.
 
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  • #2
Hmm, well, if this is anything like I'm seeing it to be, you're dealing with functions:
[tex]R_3:\mathbb{R}^2\to\mathbb{R}[/tex]
So the total differential/change of [tex]R_3[/tex] would be:
[tex] dR_3=\frac{\partial R_3}{\partial R_1} dR_1 + \frac{\partial R_3}{\partial R_2} dR_2[/tex]
 
  • #3
Actually I found it in some place as follows

d(R3)/R3= d(R1)/R1+d(R2)/R2+d(R1+R2)/(R1+R2), please let me know how it is arrived.
 
Last edited:

1. How do I calculate the equivalent resistance when resistances are parallel?

To calculate the equivalent resistance when resistances are parallel, you can use the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ....+ 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances. Or, you can use the shortcut formula Req = R1 * R2 * R3 * ... * Rn / (R1 + R2 + R3 + ... + Rn).

2. What is the effect on the equivalent resistance when resistances are added in parallel?

When resistances are added in parallel, the equivalent resistance decreases. This means that the overall resistance of the circuit decreases, allowing more current to flow through the circuit.

3. Can the equivalent resistance be less than the smallest resistance in the parallel circuit?

No, the equivalent resistance can never be less than the smallest resistance in a parallel circuit. The equivalent resistance will always be lower than the smallest resistance, but it will never be lower than the smallest resistance.

4. What happens to the current in a parallel circuit when the equivalent resistance decreases?

As the equivalent resistance decreases in a parallel circuit, the current increases. This is because the decrease in resistance allows more current to flow through the circuit, according to Ohm's Law (I = V/R).

5. Can you provide an example of how to calculate the equivalent resistance in a parallel circuit?

Sure, let's say we have two resistors in parallel, with values of 4 ohms and 6 ohms. Using the formula 1/Req = 1/R1 + 1/R2, we get 1/Req = 1/4 + 1/6. Simplifying this equation, we get 1/Req = 5/12. Inverting both sides, we get Req = 12/5, or 2.4 ohms. So, the equivalent resistance in this parallel circuit is 2.4 ohms.

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