Parallel resistanee is reciprocal of the sum?

Click For Summary
SUMMARY

The total resistance in a parallel circuit is calculated as the reciprocal of the sum of the reciprocals of individual resistances. This is derived from Ohm's Law, represented by the equation V = IR, where V remains constant across parallel resistors. The relationship can be expressed mathematically as 1/R_eq = 1/R_1 + 1/R_2 + ... This formula confirms that the total current is the sum of the currents through each resistor, necessitating the use of reciprocals for accurate total resistance calculation.

PREREQUISITES
  • Understanding of Ohm's Law (V = IR)
  • Basic knowledge of electrical circuits
  • Familiarity with resistance concepts
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of the parallel resistance formula in detail
  • Learn about series vs. parallel circuits and their characteristics
  • Explore practical applications of parallel resistances in circuit design
  • Investigate the impact of varying resistance values on total current flow
USEFUL FOR

Students studying electrical engineering, educators teaching circuit theory, and hobbyists building electronic circuits will benefit from this discussion.

Lokhtar
Messages
12
Reaction score
0

Homework Statement



Why is parallel resistance the reciprocal of all individual resistances?

Homework Equations



V=IR

The Attempt at a Solution



Well, since V is constant and I is different, you can write it as I=V/R, and since V won't change, you can make it I=V*(1/R1+1/R2),etc. So I get that, but why do you then have to take the reciprocal of all the resistances to get the total resistance? Wouldn't it just be the direct sum of the individual 1/Rs??
 
Physics news on Phys.org
Lokhtar said:

Homework Statement



Why is parallel resistance the reciprocal of all individual resistances?

Homework Equations



V=IR

The Attempt at a Solution



Well, since V is constant and I is different, you can write it as I=V/R, and since V won't change, you can make it I=V*(1/R1+1/R2),etc. So I get that, but why do you then have to take the reciprocal of all the resistances to get the total resistance? Wouldn't it just be the direct sum of the individual 1/Rs??

Because, by definition, [itex]I = V/R_{eq}[/itex]. So setting this equal to your expression, we get

[tex]\frac{1}{R_{eq}} = \frac{1}{R_1 + R_2 + \ldots}[/tex]
 

Similar threads

  • · Replies 23 ·
Replies
23
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
9
Views
1K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 24 ·
Replies
24
Views
6K
Replies
7
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 10 ·
Replies
10
Views
1K