# Increment value of equvalent resistance when the resistances are parallel

1. Jun 12, 2007

### sudhir1962

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.

2. Jun 12, 2007

### Pseudo Statistic

Hmm, well, if this is anything like I'm seeing it to be, you're dealing with functions:
$$R_3:\mathbb{R}^2\to\mathbb{R}$$
So the total differential/change of $$R_3$$ would be:
$$dR_3=\frac{\partial R_3}{\partial R_1} dR_1 + \frac{\partial R_3}{\partial R_2} dR_2$$

3. Jun 13, 2007

### sudhir1962

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: Jun 13, 2007
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